I:OP(. --~ "

Report No. FAA~D- 77 ·6

WES TR S-77-8

ANALYSIS OF PERMANENT DEFORMATIONS OF ' FLEXIBLE AIRPORT PAVEMENTS 1

Yu T. Chou

U. S. Army Engineer Waterways Experiment Station Soils and Pavements Laboratory

P. 0. Box 631, Vicksburg, Miss. 39180 .... FEBRUARY 1977 FINAL REPORT

. .

-~-• •

Document is available to the public through the National Technical Information Service,

Springfield, Va. 22151

DEPARTMENT OF DEFENSE DEPARTMENT OF THE ARMY Office, Chief of Engineers Washington D. C. 20314

Prepared for

U.S. DEPARTMENT OF TRANSPORTATION FEDERAL AVIATION ADMINISTRATION

Systems Research & Development Service Washington, D. C. 20591

·---- -~-· ------ -~ -----~- -------·-------·----~----··-----·

NOTICES

This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof.

The United States Government does not endorse products or manufacturers. Trade or manufacturers' names appear herein solely because they are con­sidered essential to the object of this report.

.·•

Technical Report Documentation Page

1. Report No. 2. Government Accession No. 3. Recipient's Catalog No.

FAA-RD-77-6 4. Title and Subtitle 5. Report Date

February 1977 ANALYSIS OF PERMANENT DEFORMATIONS OF FLEXIBLE 6. Performing Organization Code

AIRPORI' PAVEMENTS 8. Performing Orgoni zation Report No.

7. Authorl s)

Yu T. Chou TR S-77-8 9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)

u. s. Army Engineer Waterways Experiment Station Soils and Pavements Laboratory 11. Contract or Grant No.

P. o. Box 631 DOT FA73WAI-377 Vicksburg, Miss. 39180 13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address

Federal Aviation Administration Final Report Washington, D. c. 20591, and Office, Chief of Engineers, u. s. Army 14. Sponsoring Agency Code

Washington, D. c. 20314 ARD-430 15. Supplementary Notes

16. Abstract

Thi~ study was conducted to investigate the deformation characteristics of component materials in a flexible pavement system subject t.o moving airc~aft loadings, and to attempt to develop a predicti.on model to estimate permanent defvrma-tion. A J iterature survey was first conducted on the deforrr.ation characteristics of pavement component materials and the computational techniques to predict the amount of deformation. Series of laboratory repeated load tests measuring permano;;ont st_·ain were perfortned on subgrade eoil and untreated granular materials. The results were used as input to a layered elastic computer program to determine the accumulated permanent de:formation tht:it occurred in each layer of the pavement. Pavements used in the analysis were full-scale multiple-wheel heavy gear load test sections con-structed 8J1d tested at the U. S. Army Engineer Waterways Experiment Station and pavements designed by using the CBR equation.

The literature survey indicated that predicting permanent deformation in the asphaltic concrete layer is not only very costly and time-consuming but also may be incorrect. Different patterns of pe'"lll&nent strain along the asphalt layer were computed by different authoritative agencies. Results of the analysis of this study revealed that permanent deformation in the untreated granular layer cannot be predicted with a.ccur'lcy. The problem is in the difficulty of estimating stress states in the ;roranula.r materials under moving aircraft loadint;:>. .:t if..-a:5 concluded that it is no~ possible to predict the permanent de:formation that occurs in a pavement using the layered elastic computer program; thus, it was recommended that efforts be made to study the basic deformation characteristics of asphaltic concrete and taltreat~d gra;;.l..<.!~:- ~o!.ls !.n a pc~.~e~ent system e.!'!d. later initiate a develo!'Ment pr.ogram for prediction IOO.:iels when t:1e informati-:-r. 'b-eco!:!.es a~r~ilable.

The perr.:.:1.nen~ deformation occt:.rring in th~ subgrade soil of many pavements was cot.puted using the linea.r layered elastic computer program 5-nd laboratory repeated load test data. Results of the analysis indic~te that the current concept of the control of subgrade rutting in flexible pavements by the limitation of elastic strain is not strictly correct. When subgrade strain is limited, subgrade rutting may not be limited and may not be controlled.

17. Key Words 18. Distribution Statement

Layered systems Document is available to the public Pavement design through the National Technical Information Permanent deformation Service, Springfield, Va. 22151.

19. Security Classil. (of this report) 20. Security Classif. (of this page) 21· No. of Pages 22. Price

Unclassified Unclassified 116

Form DOT F 1700.7 <8-72) Reproduction of completed page authorized

PREFACE

The study described herein was jointly sponsored by the Federal

Aviation Administration as a part of Inter-Agency Agreement No. DOT

FA73WAI-377, "New Pavement Design Methodology," and by the Office, Chief

of Engineers, U. S. Army, as a part of Military Construction RDTE Project

No. 4A762719AT40, "Pavements, Soils, and Foundations," Task 02.

The study was conducted by the U. S. Army Engineer Waterways

Experiment Station (WES), Soils and Pavements Laboratory. Dr. Yu T.

Chou, under the general supervision of Messrs. James P. Sale, Richard G.

Ahlvin, Ronald L. Hutchinson, and Harry H. Ulery, Jr., was in charge of

the study and is the author of this report.

COL G. H. Hilt, CE, and COL J. L. Cannon, CE, were Directors of

WES during the conduct of this study and the preparation of this report.

Mr. F. R. Brown was Technical Director.

METRIC CONVERSI.ON FACTORS

. Approximata Conversions to Metric Me11ures "' _ ~ Approximate Coaversions fro• Metric Mea .. res

= Sy•••l W.o• Yo• bow M•ltiiiiY ., Te Fin S,_.ol Sv-•el WM• Y• ~~- M•ltiJIJ ., Te Fin Sy•••l -§----:~

- " LENGTH ~

LENGTH - nm millimeters 0.04 inches in

~ an centimeters 0.4 inches in - m meters 3.3 feet fl

in inches •z.s centimeters em - • m meters 1.1 yards yd ft feet" 30 centimeters em ..,. - km kilometers 0,6 miles mi yd yards 0.9 metsrs m ,-~---mi miles 1.6 kilometers lun = !::

AREA AREA !!l

"' - - ~ -•cen•-• 0.16 squareinclles in2

in2

squM1t inches 6.5 square centimet•s r;m2 ~ m2 ..,_. met•• 1.2 square yards yil tr -feet O.D9 square .. tors m

2 - Jtm2 - kiiCIMters 0.4 sq-. miln mi2

~ square yards 0.8 squere motors m2 .., he hecWes (10.000 mlJ 2.5 acres mi2 square miles z.e square kilometers w -

acres 0.4 hectares ha _ - ""

"' ~ MASS (waiw.t! w MASS (wei1ht! - "

- ~ g - 0.035 .......,.. oz oz ounces 28 ...,.. g = ~ kg kil- 2.2 pounds lb lb pounds 0.45 kologrems kg ~ 1 1.._5 11000 kg) 1.1 short tons

shorltons 0.9 ,.._. 1 - =-=-----(2000 lb) .. - 0

VOLUME - ~ VOLUME ... tsp tenpoans 5 milliliters mt - ml mi IIi li._s 0.03 fl_uid OUIIC»I fl oz

Tbop .. bles-s 15 millili!O<!I ml - = • I liters 2.1 pon1S = fl fl id 30 milliliters ml w I hters 1.06 quarts

oz u ounces 0.24 liters I ,.. I Jigrs 0.26 gallons .,.

pi ;::: 0.47 lihlrs I m• cubic - 35 cubic feet fl 3 qt quns 0..95 1 iters 1 - m3 cubic meters 1.3 cub1c yards yd

gal gallons 3.8 liters I ~

fl' cubic feet 0.03 cubic meters m3

- .., TEMPERATURE (exact) yil cubic yards 0.711 cuboc motors m3 ,. • •

TEMPERATURE (euct) _ ... •c Celsius 915 llhen Folorenheit "F -- • ..._...... odd32) ...._......

~F Fahrenheit 5/9 (after Celsius °C _ _ "' ~ subtracting teqMtrature _ -- "F

32) ., °F 32 98.6 212

-· - -4~,, .• ~ '•' ·14~1'•''~,.l,•~o. l' .. ~o., ..• ~~ •1 in : 2.54 te.actly). For other_exact convenuons and mc:we detai.led tables, see NBS Misc. Publ. 283, g. _. _ I _

20 0

20 ~ SO 80 !00

Units of Weights and Measures, Pr1C8 S2.25, SO Catalog No. C13.10.286. I - - S :g 37

C

TABLE OF CONTENTS

PREFACE • . . • •

CONVERSION FACTORS . . . . . . . . INTRODUCTION

BACKGROUND • • • PURPOSE AND SCOPE

LITERATURE REVIEW •

. . . . . • •

• • • • • • • • • • • • . . • • • • • •

. . ASPHALTIC CONCRETE {AC) UNTREATED GRANULAR MATERIALS • • • • • • FINE-GRAINED SOILS • • • . . . . . .

LABORATORY REPEATED LOAD TESTS

SOURCE AND DESCRIPTION OF MATERIAL • SPECIMEN PREPARATION, TESTING EQUIPMENT,

• • . .

• • • •

• •

!!!:2

• . 1

3

• • 7

• • 7 . . 9

• • • 12

. • 12 • • 33 . . 48

• • 52

• • 52

. . AND PROCEDURES • TEST RESULTS • . ' • • . . . . . . 52

54 72 COMPUTATIONS OF PERMANENT DEFORMATION

DESIGN IMPLICATIONS OF COMPUTED RESULTS •

CONCLUSIONS AND RECOMMENDATIONS •

CONCLUSIONS RECOMMENDATIONS

LIST OF NOMENCLATURE

REFERENCES

.. . . . .

• •

5

..

• •

• •

• • • • . . . • 104

. . • • 109

• • • • • 109 . . . . • 110

. . 111

. . • • • 112

INTRODUCTION

BACKGROUND

In the rational design of flexible pavements, consideration of

permanent deformation (or distortion) constitutes an important factor in

the overall design system. Excessive amounts of pavement rutting ad­

versely affect riding quality, and rutting can also cause the pavement

to crack and thus result in the loss of pavement serviceability.

Permanent deformation in a pavement is a manifestation of two

different mechanisms: densification (volume decrease) and shear deforma­

tion (plastic flow with no volume change). Monismith1 has summarized

the various forms of permanent deformation resulting from both traffic­

and nontraffic-associated causes, and these are listed in Table 1.

Excessive deformation resulting from densification can be mini­

mized by proper compaction requirements. Control of plastic flow is

actually one of the basic distress modes upon which all pavement struc­

tural designs are based. In designs of pavement systems to minimize

permanent deformation, it is general practice to place a sufficient

thickness with adequate strength of each component layer to keep the

stresses in the subgrade to a low level relative to the strength of the

soil (as in the CBR design procedure).

Since the advent of high-speed computers, two approaches have

been advocated using the layered elastic method or others to solve the

problems of design to minimize permanent deformation. One of the

approaches involves limiting the vertical compressive strain at the

subgrade surface to some tolerable amount associated with a specific

number of load repetitions (as in the Shell procedure2 ). By controlling

the characteristics of the material in the pavement section through

'materials design and proper construction procedures (unit weight or

relative compaction requirements) and by ensuring that materials of

adequate stiffness and sufficient thickness are used so that the strain

level is not exceeded, permanent deformation can be limited to a value

equal to or less than the prescribed amount. The major advantage of the

7

Table 1

Exam les of the Permanent Deformation Mode of Distress for Asphalt Pavements after Monismith

General Cause Specific Causative Factor Example of Distress

Traffic-associated Single or comparatively few excessive loads

Plastic flow (shear deformation)

Nontraffic­associated

Long-term (or static) load

Repetitive traffic load­ing (generally, large numbers of repetitions)

Expansive subgrade soil*

Compressible material underlying pavement structure

Frost-susceptible material

Creep (time­dependent) deformation

Rutting (resulting from accumulation of small permanent deformations asso­ciated with passage of wheel loads)

Swell or shrinkage

Consolidation settlement

Heave (particularly differential amounts)

* Soils in this category exhibit high shrinkage as well as swell characteristics.

8

approach is the fact that it is currently a workable tool for the pave­

ment design, and several agencies have introduced procedures based upon

it. A summary of existing criteria taken from Reference 3 is shown in

Table 2. It should be pointed out that pavements designed based on this

procedure will have sufficient thickness to protect the subgrade soil

from shear failure but not to insure that permanent deformation in the

upper pavement layers will not occur.

The other approach involves prediction of the actual amount of

deformation which might occur in the pavement system using material

characterization data developed from laboratory tests. In the new,

improved pavement design procedure4 prepared for the Office, Chief of

Engineers, U. S. Army, and the Federal Aviation Administration (FAA),

two primary distress modes, fracture and distortion, are considered.

The consideration of fatigue cracking did not fall within the purview

of this study. Rather, the prediction of accumulated permanent deforma­

tions in pavement systems under aircraft loadings was studied and the

results presented.

PURPOSE AND SCOPE

The purpose of this study was to examine the rutting characteris­

tics of pavement component materials and to develop a prediction model to

accurately estimate the amount of rutting occurring in each component

layer of a pavement system under traffic roadings.

A literature survey was first conducted on the rutting charac­

teristics of pavement component materials and the computational tech­

niques used to predict the amount of rutting. A series of laboratory

repeated load tests measuring permanent strains was performed on subgra~e

soil and untreated granular materials. The results were used in con­

junction with a layered elastic computer program to determine the accumu­

lated permanent deformation occurring in each layer of the pavement

induced by aircraft loadings. Pavements analyzed were full-scale,

multiple-wheel heavy gear load test sections constructed and tested at

the U. S. Army Engineer Waterways Experiment Station (WES) and typical

pavements as designed using the Corps of Engineers CBR equation.

Table 2

Limiting Subgrade Strain Criteria (After Yoder and Witczak3 )

Original Revised Asphalt Shell Oil Co. Shell Oil Co. Institute Kentucky Highway

Strain parameter* E E E E vs vs VS vs

Year introduced 1962-1965 1970-1972 1971-1973 1971-1973

Type pavement Highway Airfield Airfield Highway

Allo~able strain

N = 10 l-' j 0 102 -- -- 2548

103 2700 4500 1904 790

104 1680 2700 1646 639

10 5 1050 1700 1508 502

106 650 1030 1423 364

107 420 650 -- 227

108 260 4oo -- 89 00 -- -- 1060

Effective E1 , ksi 140 (thin AC) 150 100 480 (33 percent AC) 200 (thick AC) -- -- 300 (100 percent AC)

* E is maximum compressive subgrade strain, 10-6 in./in. VS

Design implications based on the results of computations were analyzed,

and recommendations for the design of flexible pavements to minimize

permanent deformations were determined.

1~

LITERATURE REVIEW

In recent years, much research effort has been devoted to the

study of permanent deformation in flexible pavements. Experience indi­

cates that under normal pavement conditions deformation within asplialtic

materials occurs only during warm weather. Under cold weather conditions,

little deformation occurs in either the asphalt material or the subgrade,

due mainly to the very stiff condition of the former. In some cases, the

subgrade soil may be frozen in the winter and provide firm support for

the overlying asphaltic concrete (AC) layer and thus reduce pavement

deformation. While rutting and fatigue are two separate modes of

distress, rutting can contribute to fatigue failure of a pavement due

to tensile strains in the surfacing which result from bending caused by

rutting in the base and sub grade.

In this chapter, reviews are presented for AC, untreated granular

materials, and fine-grained soils. A literature review was not conducted

on stabilized soils because it is the general consensus that stabilized

soils with sufficient amounts of agent experience insignificant amounts

of permanent deformation under traffic loadings.

ASPHALTIC CONCRETE (AC)

INTRODUCTION

Hofstra and Klomp5 investigated permanent deformation of AC using

a laboratory test track. The pavement structure was simplified by

utilizing full-depth AC construction with 2.0-in.,* 3.9-in., 5.6-in.,

and 7.9-in. layers of various asphalt mixes laid directly on subgrade

with a CBR of 18. The mixes had high asphalt contents to induce greater

rutting than would normally occur in practice, and a strong subgrade

was used to minimize deformation in that material.

Experiments to investigate the effect of temperature indicated

that for a 2-in. layer of AC, rutting was partly due to deformation of

the subgrade but for the 3.9- and 5.6-in. layers rutting was due entirely

* A table of factors for converting units of measurement is presented on page 3.

12

to deformation in the AC. It was found that deformation was due to

plastic flow of the material and not to densification. A range of tem­

peratures from 20 to 60° C was investigated, during which the AC modulus

decreased by a factor of approximately 60 but the permanent deformation

increased by a factor of 250 to 350.

A series of tests was carried out to investigate the mix variables

of asphalt type, asphalt content, and aggregate type. It was found that

stiffer asphalts produced mixes less susceptible to permanent deforma­

tion~ and the same effect was noted for mixes with low asphalt contents

or higher percentage of coarse aggregates. It was also found that rut

depth per wheel pass decreased with an increasing number of wheel passes.

It appeared that the mix built up a resistance to flow during the process

of deforming under repeated loading. This was probably due to the asphalt

being expelled from between aggregate particles producing greater inter­

locking, which would explain why angular aggregate produces better

performing mixes than rounded aggregates.

Studies of the distribution of permanent deformation with depth

in the AC layers showed that deformation was almost uniformly dist~ibuted

through the entire depth. Calculations of vertical strain distribution

with depth using the computer program, BISTRO, and assuming a constant

asphalt stiffness modulus showed a reasonably uniform strain distribu­

tion. However, in a 7.9-in. layer, the calculated strain was much higher

at the top of the layer than at the bottom, whereas measured permanent

deformation was only slightly higher. The strains and deformations were

not in agreement with observations of Heukelom and Klomp. 6 This could

be partly explained by the fact t.hat vertical strains measured near the

bottom of the layer were much larger than the values calculated at that

position, possibly due to the constant modulus assumed for the whole

layer.

McLean7 describes a methodology to permit estimation of permanent

deformation in pavement structures from laboratory triaxial repeated

load and creep tests. His analysis concentrated primarily on techniques

to estimate the distortion characteristics of AC and the use of these

data together with both linear elastic and linear viscoelastic theory

],3

to predict rutting in asphalt-bound layers of pavement structures. This

approach when used to study the influence of a number of parameters on

pavement response resulted in the following observations:

a. Subgrade stiffness appeared to have little influence on the accumulation of permanent deformation in the asphalt-bound layer--at least for the range in stiffnesses examined.

b. AC stiffness exerted a significant influence on rutting in the asphalt-bound layer.

c. Like the measurements of Hofstra and Klomp, 5 the calculation procedure indicated that rut depth in the asphalt layer was independent of layer thickness for the range examined.

8 Morris developed a mathematical model from the laboratory experi-

mental results to predict the rut depth of the full-depth sections at

the Brampton Test Road in Canada. The computed results match very well

with the measurements. However, Morris found that the majority of the

deformations occurred in the lower portion of asphalt layer where tensile

stresses exist. The conclusions of Morris's study were different from

those of Hofstra and Klomp5 and McLean. 7 The details of these works

will be explained in the later sections.

METHODS TO PREVENT PERMANENT DEFORMATION OF AC

The following discussion is taken from Monismith's9 study of

available methods to prevent excessive deformation in the AC layers of

a pavement.

Standing and Uniformly Moving Traffic. Two of the methods in

widespread use (presented in Corps of Engineers Technical Manual

TM 5-824-210 and California Division of Highways Materials Manual,

Test Method 30411 ) have the capability to produce reasonably performing

mixtures so long as the actual service conditions correspond to those

for which the basic criteria were developed. For conditions beyond the

realm of current procedures, the triaxial compression test has the poten­

tial to provide parameters which, when used with analyses of systems

representative of pavement structures, can provide useful design guides.

A number of investigators, as will be seen subsequently, make use of

bearing capacity relationships for. materials whose strength characteris­

tics can be represented by an equation of the form

;1.4

where

T = shear strength

c = cohesion

a = normal stress

T = c + o tan q,

q, = angle of internal friction

(1)

By performing triaxial compression tests at temperatures and rates of

loading associated with specific field conditions, the parameters c and

tP can be ascertained for design estimates. The analysis of Nijboer 12

can be helpful to properly define the parameters c and q, for design

purposes

where

and

d£1 2 cos <P

dt = 3 - sin q,

n = viscosity of mass mass d£1 dt = rate of application of axial strain

o1 , o3

=major and minor principal stresses, respectively d£1

Te = initial cohesion when dt = 0

T e

(2)

(3)

For standing loads, the value of c corresponds to

Equations 2 and 3 are used to solve for q, and c , respectively.

Data indicate that q, is relatively unaffected by rate of loading, and

both Nijboer12 and Smith13 have recommended a minimum desirable value

of 25 deg. To develop q, values equal to or greater than this, the

aggregate should be rough-textured,· angular, and well-graded.

The investigation of Nijboer can be of assistance in providing

mixtures with specific values of c necessary to satisfY particular

loading conditions. He has shown that c increases with an increase

in asphalt viscosity; is dependent on the fineness of mineral filler

15

(minus 0.00029-in. fraction); increases with an increase in the amount of

filler; increases up to a point with an increase in the amount of asphalt;

increases with an increase in the rate of loading; increases with increase

in mix density; and is dependent on the proportion of coarse aggregate

(>0.004 in.) in the mix. More specifically, Nijboer has shown that

where

c "' _y_ (FB )4.2 (Q_)-0.36 0.9 0.5 20

V =void factor [1- (air void content) 2/ 3], when the air void content = 0.03 and V = 0.9

volume filler

(4)

FB = filler-bitumen factor; i.e., 1 f"ll 1 vo ume 1 er + vo ume bitu~en D =equivalent particle size of filler (0.000004 in.)

The triaxial compression tests appear quite useful since they

provide friction ~ and cohesion c factors which, as suggested by

Nijboer.12 can be used in a solution of the Prandtl equation for a con­

tinuous strip loading:

~t = c • F(~)

where

bearing capacity, psi kg/em 2 ~t = or

F(~) = fUnction dependent on ~ ; e.g. ' for ~ = 25 deg, F(~) = 20.7

When ~t is made equal to a specific contact pressure, c and

are related as shown in Figure 1. In this figure, a mixture with a

value of c and ~ lying on or to the right of the curve would be

adequate for vehicles equipped with 100-psi tires.

(5)

~

Saal15 has suggested modification of this relationship recog­

nizing that the bearing capacity for a circular area is larger than that

for a continuous strip. The corresponding values for c and ~ ac­

cording to this relationship are also shown in Figure 1, which is

recommended-with c and ~ derived from triaxial compression tests

at slow rates of loading and high temperatures.

;1,6

35

5

0

__ y"1 eld ( according to Sao! )15

5 10 15 20

' I I I I I I L.--1 I I I I

25

Tire contact pres.;ure = 100 psi

mm1mum angle of friction according to Smith 13

30 35 L.O 45 Angle of internal friction . ¢-degrees

Figure 1. Relationship between cohesion and angle of internal friction to prevent plastic flow or overstress at a particular point in an asphalt mixture (after · McLeodl4)

],7

~~~--~------~

Smith13 has presented a relationship between c and and

bearing capacity for a circular area based on a yield criterion rather

than a plastic flow condition as in the above formulations. For the same

contact pressure, larger values of c and ~ are required than in the

previous case, as seen in Figure 1. Smith also suggests a minimum angle

of friction of 25 deg to minimize the development of instability from

repeated loading.

The relationships suggested by Saa115 would appear reasonable for

standing load conditions with c and ~ determined from triaxial com­

pression tests at a very slow rate of loading and a temperature corre­

sponding to an average high value expected in service. For moving traffic,

Smith's relationship would appear most suitable; in this case, however,

the values for c and ~ should be developed under conditions repre­

sentative of moving traffic and an average high temperature expected in

service.

Decelerating or Accelerating Loads. Results of one such analysis 14

by McLeod for a load with a contact (or tire) pressure of 100 psi are

presented in Figure 2. The terms P and Q are measures of friction

between tire and pavement and pavement and base, respectively. The

curves A and B in this figure indicate the importance of pavement thick­

ness in minimizing this form of instability when a frictionless contact

between AC surfacing and base is assumed (P - Q = 1). As the AC thick­

ness increases, the ratio t/t (ratio of length of tire tread to AC

thickness) decreases, resulting in lower values of c at a given ~

to prevent instability.

When P - Q = 0 (full friction between pavement and base--a more

practical situation in well-designed and constructed pavements) and the

thickness of the AC is in the range of 4 to 6 in. (curve C), the more

critical conditions are defined by the curve suggested by Smith13 as

shown in Figure 2.

Nijboer16 and Saa115 have considered shoving by decelerating

traffic to be the accumulation of permanent parts of successive visco­

elastic deformations and. these permanent defc:>rm.a.tions to occur above a

18

.35

30

25 Vl 0.

20 c 0 ·v; 15 Q)

.c. 0 u

5

0

Note: curves ( Al. ( 8) and (C) b-ased on relationship

'- [2/1+sinr:iJ {3tan9 +1+ 1-sin~ }+3-~~:P-Oj '· q lt-100 ·- 1-srncP 1+s!ncp

' U - pSI- C . ' ~ (P-O) tan~+ 1-srn¢>

' 1 +sin~

5

'

10 15 20 25 30 35

J. /f:2,5

-~::2.5 ).5

40 45 50 Angle of interrol friction.¢ -degrees

Figure 2. Stability curves for asRhalt mixtures subjected to braking stresses (after McLeodl )

- --------~--· -----"-------~------

shear strain of 1 percent for time and temperature conditions critical

for shoving (0.33 sec ~d 122° F for their experience),

where

Using the relationship

s min

S . = minimum stiffness mn ~

1 = 3T­y

T = shear (braking) ·stress at surface

y shear strain (1 percent)

(6)

and considering a coefficient of friction between tire and pavement of

about 0. 5, a minimum stiffness at this time and temperature of about

15,000 psi is indicated for a contact pressure of 100 psi. 17 Recent work by Valkering on the effects of multiple-wheel

systems and horizontal surface loads on pavement structures could provide

a better framework for design against shoving. Attention should be

drawn to the fact that, at high temperatures in pavements with thin AC

layers, the shear stresses at the AC/base interface will be the highest,

and that adhesion between the layers is very important if serviceability

is to be retained.

For gap-graded mixes, with a stone content in the range of 30 to

50 percent, Marais18 has suggested limiting values of various mix prop­

erties to prevent permanent deformation.

Recent developments by Shell for the solution of stresses and

deformations in layered elastic systems due to horizontal forces applied

to the pavement surface (BISAR17 ) may provide the framework for a proce­

dure to examine the influence of braking or accelerating stresses on

distortion using a procedure similar to that suggested by Heukelom and 19 .

Klomp for vertical loading.

METHOD TO PREDICT PERMANENT DEFORMATIONS OF AC

The methods presented in the previous section are limited in that

they do not give an indication of the actual amount of rutting which may

20

occur under repetitive traffic loading. Unfortunately, no method pres­

ently exists whereby such estimates can be made. Promising procedures

include the use of linear viscoelastic theory20- 22 and the use of 6 23 linear elastic theory suggested by Heukelom and Klomp, Barksdale,

and Romain.24

In the layered elastic procedure, the stresses and strains

are computed in the pavement structure and from these values permanent

deformations in each material are predicted from constitutive relation­

ships determined by laboratory repeated load triaxial tests on the

materials.

Elastic theory together with creep data from simple laboratory

tests may also be used to estimate permanent deformation. This approach

has been pursued by Shell investigators25- 27 to estimate the rutting

occurring in asphaltic layers.

In the Heukelom and Klomp procedure, the vertical strain distribu­

tion along a vertical axis is estimated within the asphalt-bound layers

utilizing layered elastic theory. Permanent deformation can then be

determined by means of the equation

where

0 p

f(e ) v

0 p

h = J

0

= permanent deformation

f( e ) dz v

= function relating the permanent strain e strain e ; i.e., e = f(e ) P v p v

(7)

to total

Such a technique appears useful at this time to assess, at least,

the effects of changes in tire pressure and/or gear configuration (and

load) on asphalt-bound layers. In addition, it may be possible to estab-

lish limiting values for e 1'

by comparing computed strains for particular

field sections for whic~ well-documented field measurements are available.

Like fatigue characteristics, howeve_r, it is highly probable that any

such criteria established for permanent deformation will be dependent on

mixture stiffness (and thus on temperature).

In this review, investigations to determine permanent deformation

at the University of Nottingham,28

, 29 University of California at 7 8 30 Berkeley, University of Waterloo, ' and at the Esso Laboratories in

France31 are discussed.

21

University of Nottingham. 28 Repeated load triaxial tests were 28 carried out by Snaith on a dense bitumen macadam. The effects of six

major variables were investigated: (a) vertical stress, (b) confining

stress, (c) temperature, (d) frequency of the vertical stress pulse,

(e) rest periods, and (f) asphalt content.

In confined tests, some samples developed longitudinal cracks

during the ~est, and all unconfined samples showed a volume increase.

The cracking was caused by the cyclic variation of tensile hoop strain

at the surface of the sample, and would contribute to volume increase

and sample failure. In confined tests, volume increase did not occur

and cracking was observed. This result is comparable to in situ condi­

tions in which restraint is offered by the large mass of material.

Hofstra and Klomp5 measured strains of up to 15 percent in situ, whereas

strains measured at failure by Snaith were only about 2 percent, sup­

porting the theory that adjacent material in situ prevents the cracking

which hastens failure of a test sample.

The effect of confining stress·was not thoroughly studied in

Snaith's investigation. Problems arose in predicting permanent strains

in the AC layers if the extreme points in the layer were considered,

since the range covered by Snaith's results only dealt with stresses

near the center of the layer. However, he suggested, as an approxima­

tion, that the layer could be considered as a whole, and stress condi­

tions at the center taken as a mean, since Hofstra and Klomp5 found that

the permanent strains were reasonably constant with depth. Snaith found

that, when considering a pavement with a 7.9-in. layer (such as that

tested by Hofstra and Klomp) that was divided into three sublayers, he

could determine the permanent strain in the two top sublayers and

obtain good agreement with measurements made in them. The computer

program BISTRO was used in the elastic analysis to calculate the

stresses and the center of each sublayer, using appropriate values of

stiffness and Poisson's ratio.

The following conclusions were drawn from Snaith's work on

repeated loading of dense bitumen macadam:

22

a.

b.

c.

d.

e.

f.

h.

i.

An increase in temperature caused a significant increase in strain.

An increase in vertical stress caused an increase in strain.

An increase in confining stress caused a decrease in strain.

The level of static confining stress which gave the same strain as the dynamic confining stress was approximately equal to the mean level of that stress.

Realistic changes in the relative lengths of vertical and confining stress pulses did not affect the strain.

The rate of strain appeared to be time-dependent at fre­quencies above 1 Hz.

Rest periods between vertical stress pulses had a negligible effect on strain.

An optimum asphalt content of 4 percent existed for maximum resistance to strain between 10 and 30° C. At 40° C better resistance was achieved with a 3 percent asphalt content.

The results obtained from laboratory tests when applied to the pavement design problem produced reasonable values of rut depth.

Conclusion h indicates the relative importance of aggregate interlock

and asphalt viscosity in resisting permanent strain. The former is

paramount at high temperatures. It should be pointed out in conclusion h

that asphalt content of 3 or 4 percent is optimum only with respect to

rutting, but may not be optimum with respect to other considerations,

such as fatigue and stability.

So far, when calculations of permanent deformations have been

made, one combination of the principal stresses has been used at the

center of each layer, whereas, in situ, this combination will change at

a particular point each time a vehicle passes. It remains to be seen

whether the adoption of a standard wheel load can accurately represent

the wide variation of random applications of wheel loads. A limited

test program is under way at Nottingham, 32 using Snaith's equipment

suitably modified, to investigate this. In particular, the effects

of temperature change and vertical stress change during a test are

being investigated.

University of California at Berkeley. 7 Repeated load triaxial

tests were carried out on AC specimens by McLean. An attempt was made

to cover the whole range of stresses to be encountered in situ by

23

adopting three types of tests to reproduce conditions at the top, center,

and bottom of an AC layer. These were triaxial extension (cycling lateral

stress only), unconfined compression (cycling vertical stress only), and

triaxial tension (cycling vertical stress in tension and lateral stress

in compression).

The permanent deformation, strain, and stress states of a 0.79-in.

layer of material such as that used by Hofstra and Klomp5 were investi­

gated by applying the theoretical model derived from the experimental 23 results and using Barksdale's approach. Good agreement with Hofstra

and Klomp's results was noted. In particular, the same form of rut

depth versus load applications curve was obtained. Figure 3 shows the

distribution of elastic stresses and strains and permanent strains with

depth for a particular condition. The similarity between the distribu­

tions of permanent strain, stress difference, and elastic strain could

be significant. Unlike the observed results of Hofstra and Klomp, the

distribution of permanent strain was not uniform, possibly due to the

simplifications adopted by McLean with regard to loading time.

The following conclusions were drawn from the investigations:

a. The subgrade stiffness appears to have little influence on the accumulation of permanent deformation in the AC layer, at least for the range of stiffness examined.

b. Asphalt concrete stiffness exerts a significant influence on rutting in the AC layer.

c. Like the measurements of Hofstra and Klomp, the calculation procedure indiGated that rut depth in the AC layer was reasonably independent of layer thickness.

University of Waterloo. 8 ' 30 Research carried out at the University

of Waterloo by Morris was based on an approach for the prediction of rut

depth using a combination of linear elastic theory and the results of

laboratory triaxial testing of AC. Two series of laboratory tests were

carried out, compression tests and tension tests. Both involved the

application of a cyclic confining stress and this was combined with

cyclic axial compressive and tensile stresses, respectively. Both

vertical and lateral deformations were measured. For the compression

tests, the vertical deformation was of interest for prediction purposes

while the lateral deformation was relevant for the tensile tests since

24

0 -~~ 2

I I £ I. .li

'/ ./v a. (l.o

D

c I

6

8 8 80 60 40 20 20 1.0 60 0

Compression Stress -psi Tension

0 0 -..... ~ v"" 2 2

( 10 20 30 40 50 60 70

Stress difference- psi

... -"""""4

~ I ,~-

v _,.. ~· = 4

~ .. J.~~ y~ 0.

Cll 0

6 .v

6

( 8 8

( 0 50 100 150 200 250 300 350 0 0·2 0·1. 0·6 0·8 1·0 1·2 1·4

Elastic strain. €v-in~r in x1Q·6 Permo nent strnin -percent at N = 5000 applications

Figure 3. Stress and strain distributions in an 8-in.-thick AC pavement subjected to a 1500-lb wheel load with 70-psi contact pressure (after McLean7)

25

it represented the vertical in situ deformation in the lower half of the

AC layer.

The results showed remarkably good agreement in view of the many

potential sources of error both in the laboratory test technique and in

the application of the results to practice. A typical result showing

the variation of permanent deformation along the pavement section is

shown in Figure 4. It can be seen that nearly all permanent deformation

in the AC layer occurred in the lower half of the layer and resulted

from the action of tensile lateral stresses, which is in contrast with

the observations of Hofstra and Klomp 5 and the predictions of McLean. 7

33 In a recent paper, Brown commented that the methods used by

Morris 30 and McLean7 may not be as sound as their good respective pre­

dictions for permanent deformation at the surface suggest. Brown sug­

gested a procedure involving the use of stress invariants which are

functions of the principal stresses, mean normal stress, and octahedral

shear stress, but are independent of the orientation of the axes. Cor­

responding strain invariants can be determined from the laboratory tests

and better estimates of the in situ vertical strain obtained.

Using this approach, some of the inherent disadvantages of the

triaxial test can be overcome. In particular, the tension zone stresses

in an asphaltic layer can be reproduced more accurately under the condi­

tions when large permanent deformations are likely. Lower temperatures

and thin layers, however, do still present a problem.

RELATIONSHIP BETWEEN RUTTING AND CREEP TESTING

The use of creep tests on asphaltic materials together with

elastic layer theory to represent the response of the pavement structure

to load is an alternative approach proposed recently by Shell investiga­

tors25-27 to estimate the amount of rutting oeeurring in the AC

layers of the pavement. Three phases may be distinguished in the work

carried out by Shell, i.e.: 31

a. A study of the creep properties of asphalt mixes. 25

b. A correlation of rutting and creep tests on asphalt mixes. 26

26

0

. c

• w 4 (.)

Lt cr: ::::> (/)

~ 6

0 _j

'~ w ~i' co

'~/ J: 8 J- ~' 0.. \ w ' 0

10

0

----<:>-- OCTOBER 1972

-->~-- OCTOBER 1970

·t COMPRESSION ZONE

NEUTRAL AXIS

TENSION ZONE

t % :'\

' ',, ,, '-...... ..._ ..._. __ ,.~

~'

o.t 0.2

PEHMANENT DEFORMATION ,ln./in. DEPTH

Figure 4. Variation of permanent deformation rate in an 11-1/2-in. AC pavement (after MorrisS)

27

0.3·

----~ ------ --~--------------

c. The systematic discrepancies observed in the second phase were studied with regard to the main points of difference between the creep and rutting tests, i.e., unconfined-confined and static-dynamic.27 A design procedure was then proposed for estimating, from the creep behavior of a mix in the labora­tory, the performance of the actual pavement based on the "predetermined criteria of the pavement deformation and desired service life."

The overall aim of the work, as stated by Hills,25 was to provide

a procedure whereby rut depth could be predicted when the asphaltic mix

and the in-service conditions are known. To this end, creep tests were

carried out in a modified version of a soil consolidation apparatus.

The ends of the specimens were lubricated by powdered graphite thus

eliminating barrelling.

Tests were carried out in a controlled temperature room at either

10, 20, or 30° C on specimens that were usually 0.79 in. in height and

2.36 in. square in cross section. Specimens were cut from a slab of the

mix. Some tests were carried out on cylindrical specimens of Marshall

dimensions, the load being applied in the axial direction. Failure of

test specimens was defined as the point at which the rate of strain in­

creased, and the experimental data given were confined to those parts of

the creep curves where the strains were less than the critical "failure"

values. Creep tests were carried out on a range of mix compositions and,

in the case of one composition, for a series of specimens that had been

compacted by various methods.

Earlier work by Shell34 , 35 had shown that for short times of

loading and low temperatures, the stiffness of the mix s . m1.x was a

fUnction only of the stiffness of the bitumen and the volume

concentration of the aggregate when the void content did not exceed

3 percent. The results reported by Hills25 indicate that, at higher

temperatures and longer times of loading, s . mJ.X

to variations in the corresponding low values of

becomes insensitive

Sbit and tends to

level out to a limiting value. Furthermore, in addition to the effect

of the volume concentration of aggregate, the gradation and shape of

the aggregate play a role and the state and method of compaction exert

a strong influence on the behavior. Other results indicate that:

28

a. In the case of two mixes with the same aggregate grading but with different asphalt contents and compacted in the same way, the mix with the lower asphalt content has a higher value of smix at any particular value of sbit •

b. The effect of substituting crushed for rounded aggregate is to produce, at low values of sbit ' higher values of smix .

c. Void content of the mix cannot be used in itself for speci­~ing the state of compaction.

Hills suggested that creep curves indicate a continuous change in

the internal structure of a mix during the course of a test, and theoreti­

cal models for the deformation were developed to take this into account.

A study of the correlation between the creep and rutting properties

of asphalt mixes in laboratory tests is described by Hills, Brien, and 26 Van de Loo. There were two types of rutting tests in both of which

a wheel was rolled on the material in a single-wheel path. In the one,

rutting tests were carried out on an indoor circular test track. A wheel

ran at a constant speed in a circular path on a track which was 27.6 in.

wide and consisted of an AC layer laid on sand compacted to give a uniform

CBR of 10. The average tire contact pressure was 72.5 psi. In the other

test, a solid rubber-tired wheel passed back and forth over an 11.8- by

11.8- by 2-in. ·AC .slab which lay on a rigid steel base. In all tests,

tire contact pressure was 117.5 psi.

To enable comparison between the results of the creep and the

rutting tests, it was necessary to express the results of both in the

same units, i.e., in terms of Smix and Sbit • For the purpose of

evaluating Smix for the rutting tests, use was made of the BISTRO com­

puter program to take into account the differences in geometry between

these tests and the creep tests together with effects due to modular

ratio between the AC layer and the supporting medium. The effect of

repeated loading was accounted for by a summation procedure in which it

was assumed that only the viscous component of the stiffness modulus of

the AC contributed to permanent deformation. The results of creep and

rutting ~s were then compared directly by plotting the stiffness

modulus of the mix smix against that of the bitumen sbit for the

creep tests and against the viscous part of the bitumen modulus

(sbit) . for the rutting tests. v~sc

29

It was concluded that, when plotted in this way, there was good

agreement between the creep and rutting curves for a variety of asphalt

mixes and test conditions and that the internal deformation mechanisms

in the mixes were the same for both rutting and creep. It was further

concluded that the analytical procedures used for the two types of test

were satisfactory. It was thus considered reasonable to make use of the

creep test in predicting the deformation that would occur under prescribed

conditions in a rutting test in which the loaded wheel runs in a single­

wheel path.

The calculated and observed rut depths for 10 mixes tested in the

tracking machine and the laboratory test track were compared. It was

found that for both kinds of rutting test and a wide range of mix types,

rut depths can be predicted from the results of creep tests within a fac­

tor of about 2 for rut depths ranging from approximately 0.04 to 0.4 in.

The results showed that the observed deviations were systematic,

and the measured deformations were generally higher than those calculated.

It was thus decided to investigate27 the main differences that exist be­

tween the two test methods; i.e., an unconfined, static test (creep) and

a confined, dynamic test (rutting experiments).

In determining S . m1.x

for the rutting tests, use was made of a

correction factor of 2 derived from an analysis using the BISTRO computer

program. To establish if this assumption of elastic behavior was in

fact an oversimplification, parking tests were carried out with a static

wheel on the test track pavement. The parking tests were carried out

for 24 hr at ambient temperature and the contact stress was taken to be

equal to that in the rutting test, i.e., 72.5 psi. A comparison of

the measured rutting and parking deformations at equal values of

(S ) indicated that the parking deformations showed the same bit vise systematic deviations from the rutting values as those calculated from

the creep test. The fact that the systematic deviations in the parking

test were almost a factor of 3 as opposed to a factor of 2 for the creep

tests suggests that the use of an "elastic" correction was a better

approximation than a procedure in which the geometry was simulated in

a continuous parking or indentation test. It was thus concluded that

30

the systematic difference between the two types of test did not result

from the use of the "elastic" correction factor or from the fact that

the one was confined and the other was not, but rather from the fact

that the one was static and the other dynamic.

The assessment of the "static-dynamic" contribution to the

observed deviation was made by carrying out unconfined creep tests, with

continuous and repeated loading. The measured total and permanent

deformations, or the stiffness of the mix derived from them (S i mx cr/emix) , were in all cases compared at equal values of Sbit and

(sbit)visc , respectively.

=

It was concluded that, with regard to permanent deformation, the

dynamic stiffness modulus of an asphalt mix is always lower than the

static one, compared at equal values of SbJ.'t and fs ) \bit vise • It was found that even in the most simple laboratory rutting

experiment (constant speed, constant load, single-wheel path, controlled

temperature) it was not possible to predict rut depth with a higher

accuracy than a factor of 2. The accurate prediction of rut depths on

the actual road was thus considered to be extremely difficult and it was

concluded that the main purpose of laboratory test methods must be

limited to the ranking of materials rather than the prediction of rut

depths.

Some creep testing was also undertaken by Snaith28 in association

with his repeated load tests. The object was to see if a relatively

simple test could be used to predict the permanent deformation under the

more complex repeated load situation. Similar ranges of vertical stress

and temperatures to those used in the repeated load tests were investi­

gated. It was intended to determine the level of static stress which

gives the same creep curve as a particular dynamic stress. This has

been done in Figure 5 where the strains after 100 and 500 sec have been

plotted against the applied stresses. It was found that at low stresses

the static and dynamic results are similar. However, at the higher

stress levels, a static stress of about 65 percent of the dynamic value

would be required to produce the same strain at a particular time.

In the creep tests, the mechanism of deformation was not compli­

cated by the cracking noted for the dynamic tests. Shorter lives would,

31

1-~ 0·8 ···--· ------·T--------··-~ h.l ()_ .. l)

S\ulic

0

3: O·G ----- -------1--------0-- --{-----l

0 0 .. -,_ OJ

,.(.J

"-0 0·'4 ------i ----c ·a ·­.. ~ V)

~ 0·21-----~-.. ~ hi > 1 KN/m

2 = 0.145 psi

o~----~~----~------~------~----~ 200 . 400 600 800 1000

i--. ...._ w t)

.oc ·w ()_

Applied vertical s.tress, KNf;y, 2

&f 1·5r---.---.---..,.--,---..:....-­V)

0 0 lO

~-

;!~ 1. Or-----J:-----+-----1--r, ·0

,b 0 ,_

.. J

V)

o Q.SJ----+---­.!-1 .. ~ ,_ QJ

>

Oyncmi~

00~----~~--~·------l __________ _j 203 1,00 GOO 800 1000

/\pptl2d. vertical strcr.s, t<.Njm2

Figure 5. Comparison of results from dynamic tests and creep tests at 20° C

3?

therefore, be expected in the dynamic case under comparable conditions.

The fact that the creep stress necessary to produce strains similar to

those in a dynamic test is 65 percent of the dynamic stress rather than

50 percent supports this.

Lateral deformations were not measured in the creep tests, so no

f 1 h bt · d Hill B · d Van de Loo26 measure o vo ume c ange was o a1ne • s, r1en, an

have, however, reported volume decreases in similar creep tests. This

suggests a different mode of failure from that occurring in the dynamic

case where dilation takes place.

UNTREATED GRANULAR MATERIALS

No effort has been made to investigate the characteristics of

deformation of pavement materials and to predict rut depths of a pavement

using rational methods until very recently. Research in this area con-23 36 37 38 39 . ducted by Barksdale, Allen, Kalcheff, Brown, and Barrett 1s

presented below.

GEORGIA INSTITUTE OF TECHNOLOGY

Barksdale23 was first to investigate the plastic deformation of

a variety of granular materials tested in the repeated triaxial cell and

developed a method for estimating the rut depth in flexible pavement.

Table 3 summarizes the 10 different kinds of base materials Barksdale

tested in the repeated load triaxial cell. The specimens were tested

to an average of 100,000 load repetitions at constant confining pressures

of 3.5 and 10 psi. The tests were performed using deviator stresses

varying from approximately 1 to 6 times the confining pressure.

The relationship for a granite gneiss (Base 6) between the axial

plastic strain occurring in the cylindrical specimens and the number

of load applications for varying deviator stresses is shown in Figure 6. The plastic strain accumulates approximately logarithmically with the

number of load applications. For very low deviator stresses, the rate

of accumulation of plastic strain tends to decrease as the number of

load applications increases. As the deviator stress increases, a

critical value is reached beyond which the rate of strain development

33

Table 3

or Material Characteristics ot l!ases Tested in the &ted Load Triaxial A at us al'ter Barksdale

Grain-Size DistrihutiOII llaximua Density liOu CharacterhHco Percent Puains Liquid Plaaticit7

I 3/4 llo. llo. Jlo. Teat Td •opt . Liait Index !!!.!. Descril!J:ion - E.. E.. !2.... SQ._ 200 ~ ...E!... percent ~ PI Claaairtcetion11

1 Orange-ton, slightl7 cl&70!7 1 100 100 100 63 Joo GHD-7 U5.lo 13.0 22 6 M(l); ~ silt)" sand

2 Lo~ silt7 fine sand ud ~ :so. ~67 crushed granite

99 85 lo2 25 13 GHD-119 138 lo.2 Bict •••• A-2-lo(O); SH

if!.els•

3 Lo% s1lt7 sand and 60% llo. L6T crurhed biotite

100 72 39 23 u 'l'-18oc 138 T.5 SIC •••• A-2-lt!oh 111

peiss

It 17% silt7 sand and 83% 95 6o 30 13 . 8 IIJlD-119 llo3 lo.6 A-2-lo(Oh Ill cro.~shed biotite g1•anite 'l'-180C llol.6 5.9 gneiss

w 5 21% sandy ail t and 79% 91 78 28 28 1lo.8 0111>-log litO 6.0 35 15 A-6(5h .. .;:-cr ... she4 biotite gr.,.ite 'l'-18oc lloO 6.3 gneiss

6 Crushed proph)"ritic 100 6o 25 9 3 OJID..II9 136 3.T granite gneiss - 3% rtneo '1-18oc l3T.Io 6.5 sOurce _\

1 Crushed p<>r;>h7rl tic 100 90 lo5 ~ 1.\.25 OHD-49 135 5.T granite gneiaa - 11.25ll T-180C 135 6.0 fines Souree" A

8 Crushed biotite granite 100 6o 25 gneiss - 3ll rtneo

9 3 ,._18oc 137 •• 6.5

Source B

9 C!"~'shed biotite granite 100 90 lo5 ~ 11.25 T-180C 135 6.0 gneiss - 11.25% tinea Source B

10 Crushed biotite grar.tte 100 90 ~o,

gneisa - 22% rtneo ~ 22 ,._180C 132.9 6.1

Source B

• I·:.Zil:llllO densit7 ol.tained b7 tile State Blshft¥ DepartMat ot Oeorlia'• teo' lletbo41 11110-T 111111 GIID-II9, eOl'1'•JiaD41111 appnlld•tel7 to AA8IIO desigr.ationa T-99 and T-180, reapec:thel7. .

•• '::he AASiiO CluoificatiOII S7ata 1o &hen tint. 111111 tho Ua1t114 &oil Clulltlcatloa BJn• e.eoall • t Soil olid in C1l;> ot Atterber& lialt deYlce,

.... z .... u a. .... ~ , .. ~ t

!

J.O r----r-~·----

1 o:~~~~ a'o.\~ I u - .... 4.1~ s. ~!)% - ·----~~

, 1 • m reF "J•IOPSI

DJ -----~-----··l

D., 1-----+----+-----J

~ D.4 -----t------1------:r-- -----+-----:::::;,(~-----1

&

~.OG NUM6ER OF LOAD REPETiliO!iS1 N

Figure 6. Influence of number of load repetitions and deviator stress ratio on plastic strain in a porphyrite granite gneiss, 3 percent fines (after Barksdale23)

tends to increase with increasing numbers of load repetitions. Further­

more, after a relatively large number of load repetitions, the specimen

may undergo an unexpected increase in the rate of plastic strain

accumulation.

To study rutting in pavement systems in a rational manner, plastic

stress-strain curves can be plotted, such as shown in Figure 7. These

curves are analogous to the stress-strain curves obtained from a series

of static tests performed at varying confining pressures. Similar

plots were also obtained for the other nine base materials. The plas­

tic stress-strain curves exhibit a typical nonlinear response. At a

given confining pressure for small values of deviator stress, plastic

strain is almost proportional to the deviator stress. As the deviator

stress becomes greater, the development of plastic strain increases

at an increasing rate until the plastic strains become very large as

the apparent yield stress of the material is reached. Elastic strain

is also strongly dependent upon the confining pressure, undergoing a

significant decrease as the confining pressure increases.

A summary comparison of the plastic stress-strain characteristics

of the base course materials investigated is given in Figure 8 for a

confining pressure of 10 psi. Although the average confining pressure

in a typical pavement structure is proba?ly less than 10 psi, the com­

parisons are shown for this value since these stress-strain curves were

more well defined. All materials compared in this figure were compacted

to 100 percent of AASHO T-180 density or its equivalent except the silty

sand which was compacted to 100 percent of AASHO T-99 density.

The base materials exhibiting by far the largest plastic strains

were Base 1, a fine silty sand base, and Base 2 which was a 40-60 soil

aggregate base. For deviator stress ratios greater than 2.5, the mea­

sured plastic strains in the silty sand were larger than those in the

40-60 soil aggregate. Base 3, which was another 40-60 soil aggregate

base, exhibited approximately one-half the plastic strain occurring

in the first 40-60 soil aggregate base due apparently to slight dif­

ferences in the soil properties. For deviator stress ratios greater

36

CD

(I) Q.

,... ~

lO

·~

u ... a: t;; a: 20 D ·-c(

> "' u

to

0

•

~·10 ...

~cr-- I I ~· s I

v~ !:··I (~

"'~L---:__j BASE I 100'.( CIID-J 710 100,000 Ill H TITIOII$ -r" l. 'ld•IIS.4pd

~ a t ". 13.4%

Jf I '•12.4%

D. I IJ u i.o u

AXIAL ru..s 11c $1111\IN , ' 1 PI:: n c E NT

Figure 7. Influence of deviator stress and confining pressure on plastic strain after 100,000 repetitions in a fine silty sand (after Barksdale23)

37

w <X>

~ I ~ .... s r::

t3 r:: ... .....

~ ..:

~

·~~ .. ··--~--..--~ .... ~~------.a~ .. ~~ .. --~--------------~----------~------------------------------~

I ~--------------t---------------J---~---- ~,~~~~ I , ·····"'~ . \,!,0\\. t-G ~____; --t-------

c

21·--~

0.4 0.1 1l AXIAL I'LASTIC $TRAIN t P, PERCENT

1CM~~ ~EPETITIC~iS 100h CO~.:~ACiiOtl

1.$ CO~t.U.CTEO co:<CITICN "3 •10 PSI

1.8

Figure 8. Summary of plastic stress-strain characteristics at 100,000 load repetitions and a confining pressure of 10 psi (after Barksdale23)

z.c

than 2.5, the average plastic strains in this soil aggregate base were,

however, still almost twice those occurring in Bases 4 and 5 which had

only approximately 20 percent soil. Fi~ure 8 shows that both soil aggre­

gate bases tested having nominally 20-80 blends had significantly better

plastic strain characteristics than did the two 40-60 bases. The plastic

strain characteristics of the graded soil aggregate bases tested in the

as-compacted condition were thus found to vary from very poor to quite

good depending apparently on the soil characteristics, the percent of

soil used in the base, and the degree of saturation.

For deviator stress ratios greater than about 2.5, the 17-83 soil

aggregate (Base 4) exhibited significantly more plastic strain than did

the best performing crushed stone (Base 6) which had 3 percent fines.

For deviator stress ratios less than 5, the plastic strains occurring

in the 21-79 blend soil aggregate (Base 5) were on the average about

20 percent less than those occurring in the best crushed stone; at

greater stress ratios, however, apparently the trend was reversed for

21-79 blend and best crushed stone.

The curves shown in Figure 8 for the crushed stone bases indicate

that the plastic strains occurring in the biotite granite gneiss (Bases 8

and 9) are greater than those in a porphyritic granite gneiss (Bases 6 and 7) for the same specified gradations. The significant influence of

an increase in percent fines and deviator stress on the plastic strains

occurring in a crushed biotite granite gneiss is illustrated in Fig-

ure 9. The plastic strains increased significantly as the percent fines

increased, with greater differences occurring at the larger deviator

stress levels.

A limited number of repeated load triaxial tests were performed

on specimens at 90, 95, and 105 percent of maximum density. The results

indicated that for all of the materials studied an average of 185 percent

increase in plastic strain occurs if the base is compacted at 95 instead

of 100 percent of maximum density. For an increase from 100 to 105 per­

cent of maximum density, the corresponding average reduction in plastic

strain was only about 10 percent. Barksdale remarked that more extensive

testing may show the effect to'.be somewhat greater.

39

3.2

2.4

1.6

0.8

0

I I

------1-··-· i I

! 3.5

COMPARISON FOR lASES

2 NOS.I,I,ID llt,IOO LOAD REPETITIONS

1111!1 T-IIDC DENSITY "J •II PSI

0 10 20 30

Figure 9. Influence of fines and deviator stress ratio on plastic strain in a crushed granite gneiss base after 100~000 load repetitions (after Barksdale2~)

4o

40

The experimental results also indicate that for all of the

materials tested an average increase in plastic strain of 68 percent

occurs when the test is performed on specimens that are soaked, as

compared with the results obtained from tests performed on specimens

in the as-compacted condition. It should be remembered that the

"soaked" specimens had a high degree of saturation but may not have

been completely saturated. These specimens were tested in a manner

which permitted a free flow of water into and out of the specimen so

that a significant buildup of pore pressure was not likely to have

occurred during application of the 100,000 load repetitions. Therefore,

if a significant buildup of pore pressure should occur in the field in

any of these materials due to poor drainage conditions, the laboratory

test results would probably underpredict the effects that soaking of

the base would have on the actual amount of rutting. Materials having

the lower permeabilities such as the silty sand and graded aggregate

bases would be more susceptible to such a pore pressure buildup in the

field.

In summary, the plastic strains of granular materials increase

with increasing ~eviator stress; decrease with increasing confining

pressures; and increase significantly with increasing fines, with greater

differences occurring at the larger deviator stress levels. Laboratory

tests also revealed that the plastic strains increased drastically if

the base is compacted at 95 instead of 100 percent of maximum density.

The failure of plastic deformation could be more serious than predicted

in the laboratory if a significant buildup of pore pressures should occur·

in the field due to poor drainage conditions.

In order for the rutting characteristics of base materials to 23 be easily compared, Barksdale proposed the concept of a rut index.

This is defined as the sum of the plastic strains in the center of the

top and bottom halves of the base, multiplied by 104. This requires

that va1u~s of deviator and confining stresses be selected for a typical

pavement, and the plastic strains obtained at a particular number of

load repetitions. Barksdale presents rut indices at 105 load repetitions

for the materials tested. These give a numerical comparison representa­

tive of the curves shown in Figure 8, and are given in Table 4.

Table 4

Summa!l of Elastic and Plastic Base Characteristics Evaluated From Rep~ated Load Triaxial Tests

Plastic Strain, 102 percent, of Cited Deviator Ruttin~ Characteristios Stress Ratio of 100 1000 Repetitions* Rut Index at Rut Potential at

Sample 100,000 ,. 1,000,000 ~ Base DescriE!ion· Condition g_,.2, ...1..:2_ 6.0"• Repetitions Repetitions

1 Silty fine sand 100% GHD-7 114 00 00 Very Large soaked

2 Soil aggregate 40-60 blend 100% GHD-49 128 270 780 1050 1130 soaked 1:':8 270 --- (Extrapolated)

3 Soil aegregate 40-60 blend 100% T-180C 58 120 285 405 467 soaked 90 190

4 Soil aggregate 17-83 blend 100% GHD-49 30 82 250 332 372 ~ soaked 36 1\)

5 Soil aggregate 21-79 blend 100% GHD-49 30 44 120 164 202 soaked ·4o 64

6 Crushed porphyrite-granite 100% T-180C 38 56 120 176 254 gneiss - Source A 3% fines 95% T-180C 50 76 170

soaked 70 114 7 Crushed porphyritic granite _lOa% T-180C 38 72 226 298 360

gneiss - Source A 11.25% 95% T-180C 126 large fines soaked 170 large

8 Crusned biotite granite 100% T-180C 36 78 100 258 292 gr.eiss - Source B 3% fines

9 CrusC.ed biotite granite 100% 'J:-180C 46 105 280 385 630 gneiss - Source ~ 11.25% fines

10 Crushed biotite granite 101.~% T-lboC 46 gneiss - Source B 22% fines

105 314 419 5520

* a 3 = 10 psi.

** These values were in most instances extrapolated from laboratory test data.

It is desirable to be able to predict rutting at higher numbers

of load repetitions, i.e., 106

or more, but, to test specimens to this

extent would be time-consuming and expensive in practice. It is thought

acceptable to extrapolate through one decade on a plastic strain versus

log number of repetitions plot and then use the results to construct

plastic stress-strain curves from which the rut potential can be esti­

mated. Rut potentials at 106 load repetitions are presented in Table 4.

The rut index and rut potential offer a rapid approximate compari­

son of rutting characteristics of base materials of the same thicknesses,

subject to the same loading and environmental conditions.

UNIVERSITY OF ILLINOIS

Allen36 conducted a series of laboratory repeated triaxial tests

on three different granular materials subjected to both constant and

variable confining pressures. Test data indicated that the nonrecoverable

deformations associated with the constant confining pressure (CCP) por­

tion of the tests exceeded those associated with the variable confining

pressure (VCP) portion for every specimen. Table 5 shows the total

plastic axial strain accumulated by each specimen during the entire test

series. It also shows the percentage of the total plastic strain accrued

during the CCP and VCP portions of each test series. From Table 5 it can

be seen that the CCP portion of each test series produced results from

2 percent to 56 percent greater plastic axial strains than the VCP portion 4o ·

test. Finn has shown that, on the basis of the Mohr-Coulomb yield

criteria for soils, plastic strain is accompanied by volume change. From

this viewpoint, the greater volume change observed during the CCP test

is compatible with the greater resultant plastic strains.

NATIONAL CRUSHED STONE ASSOCIATION

An extensive laboratory repeated triaxial test was conducted by

the National Crushed Stone Association (NCSA) to study the character­

istics of plastic deformation of graded aggregates. Kalchefr37 reported

43

Specimen

HD-1

MD-1

LD-1

HD-2

MD-2

LD-2

HD-3

MD-3

LD-3

Table 5

Percentage Total Axial Strain Accumulated During VCP and CCP Tests

Total Plastic Axial Strain e Percent e During Percent e p p p

in./in. VCP Test CCP Test

0.0036 49 51

0.0149 22 78

0.0191 48 52

0.0158 42 58

0.0173 43 57

0.0204 43 57

0.0063 49 51

0.0152 46 54

0.0193 43 57

During

that the plastic strains are greatly dependent on the degree of consoli­

dation for the same gradation, the amount and type of fines in the

gradation, the stress sequence and magnitude, and for some types of

fines the moisture content. The procedure is extremely useful for

optimizing materials combinations or for the relative ranking of dif­

ferent materials at the same stress conditions. The NCSA investigations

show that graded aggregates can be proportioned for minimum plastic

deformations to provide a base that improves its resistance to rutting

with time and one which will not crack or lose stability with age.

Figure 10 is an illustration of how density affects the plastic strains.

The load magnitude for this material was the same.

Kalcheff37 also illustrated in Figure 11 the effects of different

types of fines on the plastic response of two types of aggregates. The

gravel mix shown in the figure with either type of dust had the same

elastic properties. Kalcheff thus emphasized that all graded aggregates

44

... z L&J u 0:: w n..

... z < 0:: ... II)

0 i= II)

< ..J n..

o.r. -

D.& -

0 -102

DeN~• Tv [HLCTS VA 21A

1001 uso __ _, --------STRESS REPE:TI TIONS

~/

Figure 10. Effect of density on the plastic strain accumulations with load application (after Kalcheff37)

... z w u

5 o.s n..

... z < 0.11 tr. ... II)

u 0.3 i= II)

< ..J n..

0.2

Jol STRESS BEPETITIOUS

Figure 11. Effect of type of fines on the plastic strains of two graded aggregate bases ~after Kalcheff37)

do not have the same plastic strain responses under the same loading

conditions even though their elastic properties and the quantity of

fines may be the same. 23 Similar to the report made by Barksdale, Kalcheff also noted

the plastic strain accumulated approximately logarithmically with the

number of load repetitions. In practice the magnitude of plastic strain

which may occur during the first year would double only after about

10 years of carrying the same type of traffic. Kalcheff promoted the idea

of stage construction which will provide time for the majority of plastic

strains to take place when good clean stone base is used.

UNIVERSITY OF NOTTINGHAM

Brown38 conducted a series of laboratory repeated triaxial tests

on a crushed granite with a 0.2-in. maximum particle size. Plastic

deformations were measured for each specimen. He found that under

drained conditions the permanent strain reaches equilibrium values after

approximately 104 cycles of deviator stress. The permanent strain at

equilibrium could be related to the applied stresses by the equation

ep = 0.01 (q/cr3

) , where q is the effective deviator stress and cr3 the confining pressure.

In a recent extension of this work at Nottingham41 researchers

investigated the influence of loading sequence and that of applying

cyclic cell pressure to the same granular material. The limited study

of loading sequence showed that the resilient modulus was unaffected by

this but that permanent strain was significantly affected. The perma­

nent strain which built up after successive applications of about 105

cycles of gradually. increasing level was less than half the value

resulting when the highest stress level was applied constantly. This

finding is similar to that reported by Monismith, Ogawa, and Freeme42

for a fine-grained soil.

COMMONWEALTH SCIENTIFIC AND INDUSTRIAL RESEARCH ORGANIZA­TION, AUSTRALIA

Barrett39 examined existing data on permanent strain behavior of

base course materials in an attempt to define the variables that affect

46

the recorded material response. He commented that permanent deflection of

the pavement surface is due not only to vertical strain in each pavement

layer, but deformation also occurs transversely due to the lateral

spreading of the pavement materials. The author further commented that

the emphasis on characterization through static triaxial tests often

ignores the different structural changes that occur under trafficking

as well as stress history, reorientation of load axes, and compound

loading conditions. The use of repetitive triaxial tests to mirror

traffic conditions fails to provide for any difference between the

intermediate and minor principal stresses and for the continuous change

between the orientation of the structural and loading axes during the

trafficking. Experimental results for sands show that reorientation

of principal stress axes during cyclic shear tests produced large

increases in density. The density increase was related directly to the

magnitude of the cyclic shear strain and was virtually independent of

the normal pressure. The effect of stress reorientation in granular

materials would thus seem to be to produce larger permanent strains

than those predicted by cyclic triaxial testing. This would involve

an increase in densification with a resulting increase in stiffness

of the material and perhaps lead to stress-induced anisotropy.

Barrett also commented on the inadequacy of characterizing

granular base materials as continuum rather than as a dense, graded

assembly of oriented particles. He suggested that a particulate

approach to internal load distribution should be used to study the

deformations of granular base materials under traffic loads. The

results of such an analysis would include coupled stresses rather than

only satisfying equilibrium conditions at grain-to-grain contacts, and

would be distinctly different from those based on a nonlinear stress­

dependent continuum as is often used at present.

Barrett concluded that no model has been put forward which

would adequately characterize base course material behavior under

realistic field conditions.

47

-----~- --------------------

FINE-GRAINED SOILS

Very little work has been done investigating the permanent

deformations of fine-grained subgrade soils. Recently, Monismith, 42 Ogawa, and Freeme conducted a series of repeated load tests on

fine-grained soils to ascertain the effects of compaction conditions,

stress magnitude, and stress sequence on the accumulation of permanent

strain with repeated stress repetitions.

Test results were plotted semilogarithmically with axial,

radial, and volumetric strain against the number of stress repetitions.

Plots of change in strain per cycle showed that the rate of strain

decreases with increasing load repetitions and that permanent strain

increased with increasing deviator stress. The results also showed

that specimens compacted to near the maximum dry density tended to

deform less.

Results of the tests to investigate stress history showed that

specimens subjected to small levels of stress before being subjected to

greater stress levels deformed less than those without the conditioning

stress. A test series in which various combinations of 3, 5, and 10 psi

were applied to-specimens showed again that when the smaller stresses

are applied first the specimen deforms less.

When results were plotted on a log-log basis, straight lines were

obtained, as in Figure 12. These log-log plots strongly resemble similar

ones plotted by Snaith28 for bituminous material, and the form of the

equation developed to represent them is the same.

In practice, subgrades are generally subjected to lower stress

levels than those to which the specimens in the laboratory were subjected.

The laboratory values were chosen to obtain measurable strains. Monismith,

Ogawa, and Freeme applied the hyperbolic rule to their test results, and

found good comparison between predicted and actual curves. Deformations

at lower stress levels could then be predicted.

Equations were developed to represent the relationship between

applied stress and plastic strain at a particular number of stress

repetitions, and these may be used to predict permanent deformation in

fine-grained soils.

48

-+="' "()

"" jQI

-:-'o -X

i -~ z - ... z 1 < 0:: t-II)

..J < X <

t- -1 z 10 w z < 2 0:: w a.

102

1 101 1o2

o cr1-u3 :20 PSI

A 0"'1-o-3 :.10 PSI

0 v1-v3 = 5 PSI

water content 16-5 rv 16-S PERCENT, ~ d ., '~2 ' """" 2 - . - I .__ry 2r,s:;y II ··1 'VI J ·::> ?C;- .

confining prE-Ssure Cij = 5 ~:;; I

103 104 ,_.., ,..,-

NUMBER OF STRESS REPETITIONS

Figure 12. Relationship between permanent axial strain and number of stress repetitions (after Monismith, Ogawa, and Freeme42)

----------·---

42 Monismith, Ogawa, and Freeme also introduced the concept of

cumulative loading in this type of material, i.e., of predicting the

effect of cumulative loading in the field. There are two methods

available to obtain the cumulative permanent strain from results of

simple loading tests: a "time hardening" procedure, and a "strain

hardening" procedure. These are illustrated in Figure 13, total

deformation after N1

repetitions at cr1 and N2 repetitions at cr2 being epl + ep2 • When these two approaches were used to predict the

behavior of specimens tested with a combination of stress levels of

3, 5, and 10 psi, neither gave results that agreed quantitatively, but

they were in qualitative agreement. The time hardening procedure

provided better agreement when the stress levels were successively in­

,creased, while strain hardening gave better results when the loads

were successively decreased. These two methods can, therefore, be

used as a rough guide to bound the actual response. 43 Recently, Barker analyzed data of repetitive triaxial tests

reported by many agencies and showed that relationships exist between

permanent strain and resilient strain in these data. A procedure was

presented by which these relationships could be used for predicting the

magnitude of rutting that a pavement would develop under traffic. Pre­

dictions of rutting were made for full-scale test sections and the

predicted rut depths compared with the measured rut depths. The predicted

rut depth at low levels of traffic was greater than the measured but at

higher levels of traffic the measured rut depth was greater than the

predicted rut depth. The difference between measured and computed

values was believed to be caused by the inability to compute resilient

strains. The procedure is currently under review, and a separate study

is being conducted at WES to improve the technique to compute the

resilient strain.

50

-f: Cl c 0

E CJ

0..

Gp1 tG p2

0. w c :g Ill

.... ~ c 0 E '-Cl 0..

Ep2

I, Cp1 - .J..--

N1 Number of stress REPETITIONS

la J 'Time hardening~~' procedure

Cp2

i ____ _

€p1

Nurnber of stress REPETITION·S

( b ] 'Siroin hardening" p.-ocedure

Figure 13. Procedures to predict cumulative loading f'rom the results. of' simple loading tests (af'ter Monismith, Ogawa, and Freeme42)

LABORATORY REPEATED LOAD TESTS

The laboratory repeated load tests measuring the elastic and

permanent strains were performed on fine-grained subgrade soils and

untreated granular materials. Two series of tests were conducted on

the fine-grained soil, but tests were not conducted for AC specimens.

Details of the testing procedures and results can be found in Ref­

erences 44 and 45; however, they ~e described briefly in this report

for the convenience of discussion.

SOURCE AND'DESCRIPTION OF MATERIAL

Several representative 100-lb bag samples of the sand and gravel

subbase and crushed stone base materials were obtained from a field test

section at WES. These samples were air-dried and stored in the labora­

tory until the tests could be conducted. Sieve analyses were conducted

on representative samples of each material to determine the grain-size

distribution. Specific gravity and Atterberg limits tests were also

conducted on representative samples of each material.

The fine-grained soil was a heavy clay (CH) material which has

an LL of 73 and a PI of 48. The material is locally known as Vicksburg

buckshot clay.

SPECIMEN PREPARATION, TESTING EQUIPMENT, .AND PROCEDURES

Large molds 6 in. in diameter and 15 in. high were used in molding

the specimens of untreated granular materials. The large-diameter

specimen was chosen so that the fUll range of aggregate sizes could be

used. All specimens were compacted using a drop hammer with a 2.0-in.­

diam striking face, a weight of 10 lb, and a fall of 18 in. Specified

densities were attained by varying the number of layers per specimen

and the number of blows per layer. A triaxial cell similar to most

conventional triaxial cells was used for untreated granular soils except

that it was made sufficiently large to accommodate the large samples.

The repeated axial stress was applied to the specimen through a closed­

loop electrohydraulic-actuated piston. Program input was provided by

52

a function generator connected to the axial load controller. Loading was

applied in a haversine stress-time wave form for a 0.2-sec duration at

2-sec intervals. The actual loading applied to the specimen was

monitored internally by placing a miniature 5000-lb electronic load

cell on top of the specimen cap. Axial strains were measured inside

the chamber by an LVDT arrangement calibrated to the nearest 0.0001 in.

LVDT clamps were mounted 3.4 in. on either side of the specimen midheight

and strain was measured by monitoring the relative movement between

these two clamps. The radial strains were measured by LVDT's mounted

on the LVDT ring clamps so as to measure twice the actual radial

movement.

Two series of laboratory repeated load tests were conducted on

fine-grained soil specimens prepared at several water contents to obtain

different CBR values. The batched materials were sealed in a container

and allowed to cure for several days. Several 2.8-in.-diam by 6.0-in.­

high specimens were compacted.from each batch using CE 12 compaction

effort. Each specimen was compacted and sealed in a rubber membrane at

least 48 hr before it was tested. This was done to insure that the

water content was uniform throughout the specimen. One CBR specimen

was prepared from each batch using the CE 12 compaction effort so that

laboratory CBR tests could be conducted. A conventional triaxial cell

was used for testing, and the repeated axial stress was applied pneumat­

ically. Loading was applied in a trapezoid stress-time wave form for

a 0.2-sec duration at 2-sec intervals. The loading was monitored by

placing a miniature electronic load cell on top of the specimen cap.

Axial strains were measured over the central 4 in. of the specimen by

an LVDT arrangement. LVDT ring clamps were placed approximately 1 in.

from each end of the specimen and strain was measured by monitoring

the relative movement between these two clamps. Radial strains were

not measured. Frictionless end platens, incorporating a layer of Teflon

between the end platens and the specimen, were used to minimize end

restraint effects. A membrane was placed on each specimen to minimize

the loss of moisture during testing. No confining pressure was used in

the first series of tests, but a constant confining pressure of 2 psi

53

~~~~------~-----

was used in the second series of tests. The details of the equipment

can be found in References 44 and 45. Prior to the repeated load tests, an unconfined compression test

was conducted on the fine-grained soil to determine its compressive

strength. The applied repeated load stress equal to or less than

70 percent of the unconfined compressive strength was used in conducting

the repeated load tests. Higher stress near the failure strength of

the soil was not used in the tests.

TEST RESULTS

During the laboratory repeated load tests, both elastic (resilient)

and plastic (pe;manent) strains were measured. Analyses were made on these

measured values. The details can be found in References 43, 44, and 45. In this section, only the permanent strain data are presented and analyzed.

Figures 14 and 15 show the accumulated plastic strains for crushed

limestone base and gravelly sand subbase materials. The specimens were

prepared in a uniform condition, but small variations in density were

observed. Two expressions of stress ratios were used in the analysis.

One is the ratio of deviator stress to confining stress (cr1 - a3

)!a3

,

and the other is the ratio of octahedral shear stress to octahedral

normal stress 'oct/croct • It was found that the use of octahedral

stresses was more advantageous in this study. They will be discussed

later in the report. The expressions for the octahedral shear stress

and octahedral normal stress are shown below, respectively.

'oct = ~ ~ (crl - 0 2)2

+ (cr2 - 0 3)2

+ (crl - 0 3)3

0 oct = ~ (crl + 0 2 + 0 3)

where cr1 , cr2 , and cr3

are the major, intermediate, and minor

principal stresses, respectively •.

(8)

(9)

Figures 14 and 15 show that the permanent deformation of untreated

granular materials increases with increasing load repetitions and stress

intensity, but decreases as the confining pressure is increased. The

inconsistencies of same data may be due to the variations in density.

1-z w u 0::

"" n.

1.4

.. 1.2

1.0'

... 0.8 z < 0:: t­Il)

u t-II)

< ..J D.

0.6

0.4

0.2

0

~CCIII.(N

- ~ e

. 10 12 ...

ryn llj ··I I rrn Ill I I jllllj I I I jlllll Cii o; -o-, v, o; -o-, ()oct Toct lodj<roct rs• PSI "G'; -c,;;-- PSI PSI· ------40 119.0 3.90 2.90 79.7 55,9 0.70 2~ 110.5 !U4 4.74 64.5 55.7 0.86 10 46.3 5.83 4.03 26.1 22.7 0.87 20 43.0 3.15 2.15 34.3 20.2 0.59

10 100 1000 10000

STRESS REPETITIONS

Figure 14. Accumulated plastic strains for crushed limestone specimens

100000

t-z t.J u a; t.J a.

... z < a; l-Cl)

u 1-Cl)

~ ...J n.

-, I jllllj Gj v,-cr, PSI PSI

0.6 3 20 42.5 0 10 40.5 10 10 4G.3 12 20 .0:3.0

0.4

0.2

.1 I I jllllj SJ•- ~ (Jod

Cf'?. PSI ·--2.12 2.26 4.85 3.56

3 4.2 17.5 26.2 21.7

20.0 10.6 22,8

6.5

0·58 } GRAVELLY SAND 0,61 0 •87 1- LIMESTONE o. 76j

0 ~~~~~~'~'.~ll~i--~~~~~~~~~ll~j--~~~~~~w~~--~~~~~--~~~~~ 10 100 1000 10000

STRESS REPETITIONS

Figure 15. Accumulated plastic strains for gravelly sand and crushed limestone specimens

100000

For instance, Specimens 5 and 8 in Figure 14 had nearly the same stress

ratios but had different densities. The accumulated plastic strain for

Specimen 8 (137.1-pcf density) was much higher than that for Specimen 5

(141.9-pcf density).

Figures 16a-16d show the permanent deformations of fine-grained

soils having four different CBR values in the first series of tests. The

CBR values were 2.4, 3.2, 5.4, and 6.3, as shown in Figures 16a, 16b,

16c, and 16d, respectively. The water contents, dry densities, and other

information of each specimen tested are listed in Table 6. The repeated

load tests were conducted with zero confining pressure, and the tests

were carried out only up to 1000 repetitions.

Figures 17a-17e show the permanent deformations of fine-grained

soils of three different CBR values in the second series of tests. The

CBR values were 3.7, 7.5, and 13.8. The water contents, dry densities,

and other information for each specimen tested are listed in Table 7.

A constant confining pressure of 2 psi was applied to the specimens

during the tests and the tests were carried out to 50,000 repetitions.

Results for both series of tests shown in Figures 16 and 17

indicate that the permanent strain increases with an increase in load

repetitions, and increases rapidly with an increase in load intensity.

Figure 18 shows the relation between permanent strain and load intensity

at four CBR values for the soils of the first series of tests. The load

repetition level was eXtrapolated to 5000. It can be seen that as the

CBR of the soil increases, the soil's resistance to permanent deformation

increases rapidly.

Elastic strains were measured in each soil specimen during the

tests. Figure 19a shows the relationships between the elastic and

permanent strains measured at 1,000 repetitions for soil specimens from

the first series of tests. Figure 19b shows the relationships at

50,000 repetitions from the second series of tests. It can be seen that

the permanent strain increases with increasing elastic strains, and at

a given elastic strain, the permanent strain increases with decreasing

soil strength. Similar relationships are also found for other strain

repetitions. The significance of this observation will be discussed

later.

57

0.7

O.G

0.5 ,_ z .., u

-= "" ::.. .. ~ o . .;

"" ~ < ·:::: .... .., ..J

V1 ~ 0.3 ():) >< < ~ .... .., < .l c.

.LEGEND =

REPEATED SPE:CIMEN STRESS

SYVRO!:. NO. PSI

• &

I 0 A

II 2.70 12 <L~4

13 3.37 15 1,44 10 4,14

CBR=2.40 MOISTURE CONTENT-: 3l.l ~-

5

Figure 16a. Accumulated plastic strains for fine-grained soil, CBR = 2.4, first series of tests

V1 '\0

.. z w u a: .., CL

0.7

o.~

0.5

~ o.~ ... ~ -< c: .... r -' ~ O.J )(

-< u

~.J

LEGEND

REPEATED SPECIMEN -STRESS

sv~ NO. PSI

• 8 2.~0

A 9 ~.25

• 10 4.10 0 14 5.70

CBR=3.23 MOISTURE COHTEHT=31.0~

!0~

for fine-grained soils,

0.7

O.CI

o., ,.. z w \) a: ..: c. .. .!" 0.4

~ < c: t-.,

0'. ..J O· ~ 0.3

>(

< ~ t-., < ..J c.

0.2

0.1

.LEGEND

REPEATED SPtCIMtN STRESS

SYMI!Ot. NO. PSI

• .& I 0

4 5 6 18

C8R:5.(4 MOISTURE CONTENT= 28.7"

5.2 7.7 10.0 II. 7

NUMO(R OF REPETITIONS

Figure 16c. Accumulated plastic strains for fine-grained soil, CBR = 5.44, first series of tests

'·"'

1.2

1.0 ,_ z

·W u c: .., CL .. ~ o.e -~ < c: ~ .r.

0\ .J ..... ~ 0.0 )(

< !::1 ""' ., < c:

0.4

LEGEND

REPEATED SPECIMEN STRESS

SYMDO\.. NO. PSI

• I 12.7

" 2 16.1· 11 3 JILl 0 7 9.1 4 17 12.1

CBR =6.26 II.OISTURE CONTENT=27.6%

NUMBER OF REPETITIONS

Figure 16d. Accumulated plastic strains for fine-grained soil, CBR = 6. 26,' first series of tests

Table 6

First Series of Tests

Moisture Dry Cycled Specimen Content Density Saturation Stress CBR at

No. percent pcf percent psi 0.1-in. Penetration

Batch I

1 27.6 93.0 92.4 12.7 2 27.7 92.4 91.1 16.1 3 27.9 92.1 91.4 16.1 7 27.4 92.1 89.6 9.1

17 27.1 93.1 90.8 12.1 CBR-I 27.6 94.1 .22.:...Q. 6.26

Average 27.6 92.8 91.7

Batch II

4 28.7 91.6 92.7 5.2 5 28.7 91.6 92.7 7.7 6 28.8 90.9 91.7 10.6

18 28.6 91.9 91.9 11.7 CBR-II 28.7 92.9 95.3 5.44

Average 28.7 91.8 92.9

Batch III

8 30.9 88.8 93.2 2.50 9 31.0 88.9 94.0 5.25

10 30.8 89.0 93.4 4.10 14 31.2 88.5 93.4 5.70

CBR-III 31.1 88.2 92.4 3.23

Average 31.0 88.7 93.3

Batch IV

11 33.1 85.8 93.0 2.70 12 33.3 85.7 93.0 2.34 13 33.3 85.8 93.7 3.37 15 33.1 85.9 93.2 1.44 16 32.7 86.3 93.0 4.14

CBR-IV 33.5 85.8 94.3 2.40

Average 33.1 85.9 93.4

62

0'\ w

t-z IIJ v c: w r..

...

~7,

~·l o.~

.., .. 0.4

~ < c: ~ &1'1

-' ~ Q.l >(

< y ~ ~.,

< -' Cl.

0.2

LEQ.Q!.Q

REPEATED-·sTRESS

SPECIMEN u, . u, SYMSO!,. NO. ~

0 9 3.64

0 11 2.27

CBR=3.7

l5.d ~OF UNCONFINED COMPRESSIVE STRENC"l"H

10

NUMaER OF REPETITIONS

Figure 17a. Accumulated plastic strains for fine-grained soil, CBR = 3.7, second series of tests

0\ +="

!Aj

1.2 ....

1.0

""' z ..., u c: ..., ~

~ 0.8 -~ < c: t; _, ~ 0.6 )(

< \)

t= "' < _, Q.

0.~

~ A v .

LEG!O:NO

REPEATED SoRESS

SPECIMEN c-, • c-, !::.Q.,_ _n.r. 10 6.119

12 8.75

CSR =3.7

45 "-OF UNCC'NFINED COMPRESSIVE STRENGTH . .

01 I J I I I I J I I I I I I I I 1 I I I I I I I I I It I I I I I I I J I I I I I [I • II

I 10 100 11000 101000 ICO,OOO NUM13E:R OF REPETITIONS

Figure lTb. Accumulated plastic strains for fine-grained soil, CBR = 3.7, second series of tests

0\ 'Vl

0.7

0.0

.. o.~

% l.oJ u c:: w 0. ...

..: 0.4 z <: c:: .... ..., ..J < x 0.3 < .U .... ..., < ..J c.

0.2

SYM90!,

0

0 9

LEGENO

REPEATED STRESS

SPECIMEN u, · o 3 ~~ s 10.00

7 4.63

8 16.97

· CBR=7.5 j·

SS.O ~~OF UNCONFINED COMPRESSIVE STRENGTH

ob ' · 1 r 11 1 cQ 1 1 1 1 1 1 1 t9- 1 1 1 ' 1 1 !! 1 1" , 1 r , 1 ' q 1 I 10 100 1,000 10,000

NUMOER OF l'!EPETITIONS

Figure l7c. Accumulated plastic strains for fine-grained soil, CBR = 7.5, second series of tests

;co, coo

0'\ 0'\

... z "' v c:: w c.. ..

0.7

0.0

0.~

~ 0.< .... ~ < a: s; ..J ~ '>(

< v ~ ., < ..J c..

03

0.2

0.1

SYMBOL

6

LEGEND

REPEATED STRESS

SPECIMEN o-, • C'' ~~

6 21.6

CBR=7.5

70 ~OF UNCONFINED COMPRESSIVE STRENGTH

O : I I I I I I I I_ I_ I I I I I I I I I I I I I I I I I I I I t I I I I I I I I ! r ! I t I I 100 r,ooo 1o,ooo ICC,CCO

NUMSC:R OF REPETITlONS

Figure 17d. Accumulated plastic strains for fine-grained soil, CBR = 7.5, second series of tests

0\ -~

..

LEGENO

REPEATED ·sTRESS

SPECIMEN cr1 • cr1 SVMBOI.. NO. ~

0 1 13.60

A 2 27.50

... 0., c 3 5.69

z "'

v 4 21.91

u c: "' CBR= 13.8 D.

... .: 0.-4

~ 70 " OF UNCONFtNEO COMPRESSIVE STRENGTH < a: t-., .J < x 0.3 < ~ t-., .< .J Q.

0.'2

0.1

o! I 1!9•11(9 1 111111;, ''~'Ill!''' I 10 100 11000 lO,OCO IC01 0CO

NUM3ER OF REPETITIONS

Figure 17e. Accumulated plastic strains for fine-grained soil, CBR = 13.8; second series of tests

Specimen No.

1 19 2 20 3 21 4 22

Average of Specimens

CBR

5 23 6 24 7 25 8 26

Average of Specimens

CBR

9 27 10 28 11 29 12 30

Average of Specimens

CBR

Table 7

S ecimen Identification and Com osition Data Second Series of Tests

Moisture Dry Cycled Content Density Saturation* Stress UCS** :percent :pcf :percent psi :percent

Batch V

25.43 96.27 91.90 13.8 35 23.24 97.7 86.95 27.5 70 24.17 95.95 86.70 5.89 15 23.19 96.64 86.45 21.91 55.8

24.13 96.64 88.0 23.2 98.2

Batch VI

26.78 94.77 93.26 10.0 32.4 26.77 94.89 93.59 21.6 70 26.69 95.52 94.16 4.63 15 26.83 94.96 93.92 16.97 !L_

26.77 95.04 93.73 26.0 95.9

Batch VII

31.0 89.15 94.38 3.64 25.3 30.45 89.97 94.52 6.50 45 30.55 89.83 94.53 2.27 15 29.69 91.15 94.83 8.73 6o

30.42 90.03 94.57 30.4 90.0

* Based on Gs = 2.69 est.

CBR at 0.1-in.

Penetration

ucs = 39.3

13.8

ucs = 30.9

7.5

ucs = 14.4

3.7

** Percent of unconfined compressive strength (UCS) represented by cycled stress.

68

0'\ \D-

z ""'-;.. z

,.., •o

8

... 6 Q.

c.v

z < 0::: I- 4 cf)

_J

< X < u 1-cf)

< _J c...

2

5000 LOAD REPETITIONS cr3 =o

-----:-,----:~-~ I ~ I I I

4 6 8 10 12 14 16 G11 PSI

Figure 18. Relationships between plastic strain and stress intensity, first series of tests

. ~ •n .......... . ~ •n ,-...

II) (Y') ~ I 0 0 •n rl +' •n .. +'

Q) p..p..

w Q) p:;

~ ~ ·n •n ro ro J.< J.< +' t'C lf.)

'td 0 0

•n 0

:1 .-I

0 ~ •n ......... +' II)

aS rl p..

~-------------~---

0.1-·~,------~--~--~~~~~~------_. ____ L-_.~~~~~ 0.1

-3 I Elastic Strain cR , 10 in. in.

Figure 19a. Relationships between plastic strain and elastic strain for fine-grained soil at 1000 repetitions, first series of tests

70

10-

50,000 RE:PEIITIONS (;3=2.0 PSI

Figure 19b. Relationship between plastic strain and resilient strain for fine-grained soil at 50,000 repetitions second series of tests

Results of the first series of tests (Figure 16) were much more

consistent than those of the second series (Figure 17). Figure lTb

(CBR = 3.7) indicates that the permanent strains for a specimen subjected

to a deviator stress of 6.49 psi (Specimen 10) were greater than those

for a specimen subjected to a deviator stress of 8.75 psi. This is

obviously due to the wide difference in water content of the specimens.

Also shown in Figure 17a, the permanent strains for a specimen subjected

to a deviator stress of 2.27 psi (Specimen 11) were greater than those of

a specimen subjected to a deviator stress of 3.64 psi (Specimen 9), while

the water contents of the two specimens were nearly the same.

COMPUTATIONS OF PERMANENT DEFORMATION

METHODOLOGY

A number of procedures are available to estimate the amount of

permanent deformation resulting from repeated traffic loads. They may

be categorized as:

a. Use of an elastic layered system to represent the pavement structure and materials characterization by:

(1) Repeated load triaxial tests.

(2) Creep tests (not for untreated granular materials).

b. Use of a viscoelastic layered system to represent the pave­ment structure and materials characterization by means of creep tests.

Since linear layered elastic program has been used by many

researchers, such as Monismith,1 McLean,7 Morris,8 Barksdale,23 Brown,

Pell, and Brodrick, 32 Snaith, 28 and Hofstra and Klomp, 5 it was decided

that it would be used along with laboratory repeated load tests in this

study. The layered elastic program used in this study is described in

Reference 46 and only linear behavior is considered.

Monismith1 proposed that, to use the layered elastic analysis,

relationships between plastic strain and applied stress must be available

for each of the pavement component materials; i.e.,

72

where

Ep = plastic or permanent strain

crij = stress state

(10)

For a particular layer, it is then possible to estimate the

permanent deformation occurring in that layer. This is done by computing

the permanent strain at a number of points within the layer, the number

being sufficient to reasonably define the strain variation with depth.

Permanent deformation is then determined by summing the products of the

average permanent strains and the corresponding difference in depths

between the locations at which the strains were determined (Figure 20),

i.e. ,

where

(11)

p . th oi(x, y) =permanent deformation in the i. position at

point (x, y) in the horizontal plane

( + D.Z2i) Ef = average permanent strain at depth Zi

D.Z. =difference in depth (or the thickness of the layer) l.

Total permanent deformation may be estimated by summing the contributions

from each layer.

With the knowledge of .plastic strain at various numbers of load

repetitions, the development of permanent deformation with traffic can

thus be estimated. In this study, D.Z. was taken as 6 to 8 in. in the l.

granular layer, and was a variable in the subgrade. The thickness of

the layers used in the computations D.Z. , measuring down from the sub-l.

grade surface, were 10, 10, 10, 20, 20, 20, 50, 50, 100, 100, 100, and

200 in. The stress intensities became very small below that depth. For

single-wheel loads, the permanent strains were computed at points along

73

o;

~------------------------------~y

I'

~p ----......-----

·····£/' .1r,

Ei --~-~----

£j ____ ...;·'-------• • • • • •

(p---------·--------n

Figure 20. Schematic representation of pavement system used to estimate permanent deformation (after Monismithl)

74

the load axis. For multiple-wheel loads, the permanent strains were com­

puted at points along the vertical axis at the centroid of the Boeing 747

twin-tandem assembly and at points along the vertical axis under one of

the inner wheels in the second row of the C-5A 12-wheel assembly, where

the computed values are generally the maximum. The gear configurations

for a C-5A 12-wheel gear assembly and a Boeing 747 twin-tandem gear

assembly are shown in Figure 21. To compute the stress states using the

layered elastic computer program, the selections of modulus values for

AC, unbound granular materials, and subgrade soils are explained below.

ASPHALTIC CONCRETE (AC)

Because of the thermo-viscoelastic nature of asphaltic materials,

the most important factors influencing the stress-strain relationships

are temperature and rate of loading. The resilient moduli of asphaltic

materials should be evaluated in the laboratory at different temperatures

and at different rates of loading. However, such data for the actual

asphaltic mixtures were not available during the preparation of this

report; therefore, resilient moduli of asphaltic mixtures developed

by T~e Asphalt Institute were used. 47 For each test pavement, a mean

temperature versus depth relation for the entire traffic period was

determined and was used in the computations. For pavements designed

by the CBR equation, moduli of 140,000, 150,000, and 160,000 psi were

selected for AC layers having thicknesses of 2, 3, and 4 in., respec­

tively. In the computatio~s, Poisson's ratio of 0.4 was used for all

asphaltic mixtures.

UNTREATED GRANULAR MATERIALS

The modulus ratios of the untreated granular layer to the subgrade

used by The Asphalt Institute48

were adopted in this study. The ratios

were used by The Asphalt Institute in the development of subgrade failure

criterion of the full-depth AC airfield pavements based in part on the

analysis of Corps of Engineers field test data. The ratios used were

2.9, 2.3, and 1.8 for CBR's of 3, 5, and 10, respectively. The values

were selected from a theoretical study of the stress dependence of the

75

285° 155°

65°

TWIN-TANDEM ONE TWIN-TANDEM COMPONENT Of 747 ASSEMBLY

TWELVE WHEEL ONE MAIN GEAR Of C-SA

Figure 21. Wheel arrangements for twelve-wheel and twin-tandem assemblies

resilient modulus of the granular layers, as evaluated from laboratory

tests. Studies conducted at WES have found that these modulus ratios

are very reasonable for Corps of Engineers and FAA type pavements; i.e.,

3-in. AC surface, 6-in. crushed stone base, and a thick sand and gravel

subbase. In the computations, Poisson's ratio of 0.45 was used. It will

be seen later that the criterion developed using these ratios is very

close to that developed by The Asphalt Institute (shown in Table 2).

SUBGRADE SOILS

The empirical relation E = 1500 CBR was used in the analysis

to determine the moduli of subgrade soils. 49 A discussion of the adequacy

of this relationship for characterizing subgrade soils can be found in

the review of the state of the art in material characterization. 50

Poisson's ratio of 0.4 was used in the computations.

TEST PAVEMENTS

Table 8 gives test data for 11 selected test pavements under

multiple-wheel heavy gear loads. The pavements were trafficked by

prototype loadings of a 12-wheel assembly (one main gear of a C-5A) and

a twin-tandem assembly (one twin-tandem component of a Boeing 747). All

test pavements were constructed over a 4-CBR subgrade soil, except test

pavements 2 and 6 in which an extra-weak layer (3 ft) of 2-CBR material

was placed 21 in. below the surface of the 4-CBR subgrade. The purpose

of this arrangement in the test program was to determine possible effects

of a deep soft layer beneath very heavy multiple-wheel aircraft. The

results of the multiple-wheel heavy gear load tests51 revealed that the

existence of a deep soft layer in the pavement has no significant effect

on the overall performance. The failure coverage of each pavement shown

in Table 8 was determined when either of the following two conditions

occurred:

a. Surface upheaval of 1 in. or greater of the pavement adjacent to the traffic lane (pavement shear failure).

b. Severe surface cracking to significant depths.

Surface rutting was not considered in the failure criterion; however,

this has a vital significance in the design considerations of rutting.

It will be discussed further in this report.

77

Table 8

Multiple-Wheel Data

Assembly Coverages Test Aircraft Load Tire Contact Thickness 2 in. Subgrade at

Pavement Type kips A . 2 Surface Base Subbase CBR Failure rea, 1n.

1 Boeing 747 240 290 3 6 24 3.8 4o

2* Boeing 747 240 290 3 6 24 4 4o

3 Boeing 747 240 290 3 6 32 4 280

4 C-5A 360 285 3 6 6 3.7 8

~ 5 C-5A 360 285 3 6 24 3.8 1500

<X> 6* 360 285 6 24 4 C-5A 3 1500

7 C-5A 360 285 3 12** 0 4 98

8 C-5A 360 285 15 0 0 4 425

9 C-5A 360 285 3 6 15 4 104

10 C-5A 360 285 9 0 15 4 734

11 C-5A 360 285 9 15** 0 4 2198

Note: 1 kip = 4.44822 kN; 1 in. 2 = 6.451600 em. 2

* A 3-ft-thick layer of 2-CBR soil was placed 21 in. below the subgrade surface.

** Asphalt-stabilized.

In the use of laboratory repeated load test data (as shown in

Figures 13-16) to compute the permanent deformations occurring in the

pavement induced by the traffic loads, 1 coverage in the field is assumed

to be equal to 1 strain repetition in the laboratory. •Concerning the

lateral distribution characteristics of aircraft or runways, this

assumption is not correct. However, as will be seen later, this

assumption would not change the conclusions derived from this study.

RESULTS

AC Surfacing. Computations of permanent deformations were not

made on the AC surfacing due to the following reason: The present state

of knowledge on the prediction of permanent deformations of AC is still

in its infancy. Controversial concepts and different results have been

presented by different agencies.7 •8 In a recent paper, Brown33 suggested

an improved approach to overcome some of the inherent disadvantages of

the laboratory triaxial test. However, Brown admitted that for lower

temperatures and thin layers, the approach still has inadequacies. It

was thus decided to concentrate the effort to the study of permanent

deformations only .in untreated granular materials and subgrade soils.

Untreated Granular Materials. Difficulty was encountered in the

computations of permanent deformations in granular materials due to the

fact that the stresses computed by the linear layered elastic program

do not truly represent field conditions.

Thampson52 in utilizing layered elastic theory for computing

stresses in granular materials under highway pavements encountered the

same difficulty and made the following statement:

According to these calculations a small amount of tension develops in the base. However, it has been stated previously that this particular base material cannot take tension and yet the unsoaked pavements did not deteriorate significantly. Therefore, it is suggested that the particles of the-base move, and the stresses are redistributed so that no-tension exists.

Also, Morgan and Scala, 53 in a review of flexible pavement behavior and

application of elastic theory to pavement analysis, came to the following

conclusion:

79

The general failure of two- and three-layer systems to satisfy the Burmister prediction appears to be due to lower­than-expected modulus for the stiffer layers resulting from their inability to withstand tension, or their dependence on confining stress which may not be sufficient.

Even when nonlinear finite element analysis is applied to airport

pavement analysis, stresses are computed which violate accepted failure

laws. In such an analysis, Barker54 makes the following statement:

Tensile stresses were generated in the granular material to such an extent that the pavement response (referring to computed response) was dictated more by limiting minimum moduli than by true material properties. The field data indicated much better performance of the granular material under the high loads than was indicated by the finite element analysis. The most plausible explanation is that a marked increase in Poisson's ratio probably occurred as the granular material approached failure. The increase of Poisson's ratio in the crushed stone would be greater than the increase in the sandy gravel and could explain the better comparative perform­ance of this material than was indicated in the analysis. It is felt that at near failure Poisson's ratio for both mate­rials go above 0.5 and thus generate additional complications in the analysis of heavily loaded pavement systems.

Prior to further discussion, it will be beneficial to present

~he experience gained from this study.

a. When the layered elastic computer programs were used to obtain information on the stress states in the pavement structures, tensile radial stresses were generally computed at the bottom layers of the granular materials. This posed a serious prob­lem in the use of laboratory repeated load test data.

b. In conducting laboratory repeated load tests on untreated granular materials, confining pressures were required during the test to prevent the specimen from collapsing under the load applications. The magnitude of the required confining pressure cr3 depended upon the magnitude of the applied vertical pressure cr1 . In general, the ratio of cr1/cr3 could not exceed a value of 5. In other words, if the applied vertical stress cr1 was 20 psi, the confining stress cr

3 must be kept at 4 psi or greater.

When the stress states in the granular layers were computed and

expressed by the relation (cr1 - cr3

)/cr3

(as shown in Figures 14 and 15),

the expression becomes negative when tensile radial stresses cr3

were

Consequently, the laboratory repeated load test data cou~d computed.

not be used to estimate the permanent strains because the tests were

80

conducted with compressive confining pressures; i.e., o3

was always

positive. To circumvent the situation, the ratios of octahedral shear

stress to octahedral normal stress T /o were used. oct oct The advantage

of this expression is that the stress ratio was always positive even

though the value of o3

was negative. This can be readily seen in

Equations 8 and 9. In using Equations 8 and 9, the intermediate stress

o2 was equal to the minor principal stress o3

Although the octahedral stress ratios eliminated the problem

caused by the negative confining stress o3

, difficulties still

existed. Figure 22 shows the relationships between permanent strain

and octahedral stress ratio plotted for 5000 strain repetitions. It

can be seen that the octahedral stress ratios for specimens tested in

the laboratory have magnitudes less than one, and the rate of increase

of permanent strain with stress ratio is very rapid. However, the

stress ratios computed using linear layered elastic computer programs

have values greater than three in most cases. Extrapolations have to

be used to estimate the permanent strains at high stress ratios. It

can be seen in Figure 22 that the extrapolation to a stress ratio of

two is beyond the acceptable confidence level.

The problem of estimating permanent deformations in granular

layers using a mechanistic approach, such as the one used in this study,

lies in the difficulty of computing the stress states. It is believed

that when heavy wheel loads are applied on the pavement surface, radial

tensile stresses tend to develop at the lower part of the granular base

layer and slip of the material becomes incipient. The granular mate­

rial can sustain a certain amount of tensile stresses which are resisted

by frictional stresses developed between the granular particles caused

by the vertical compressive stresses that exist in the base. Once the

material starts to slip, passive pressure due to overburden will be

mobilized and the confining pressure will be increased. Consequently,

the moduli of the granular materials will increase. Since granular

particles will separate under tensile stress and since granular layers

in a well-constructed pavement do not fail under a few passes of traffic

loads, the author believes that the large radial tensile stresses in

~ ., t

··C~,o . " .... f! ~

~ ..... ~ Cl ....

= £

l-6

I .A

1.2

1.0 0

o.a Crushed Limestone ---...:..

0..6

OA

0.2

I I I I I I I I I

I Gravelly Sand-/

I I I I I I

0 - . ...-c::;...---+----+-----4 0 o.s 1.0 1.5

Octahedral Stress HlitiO T t/a t oc oc

Figure 22. Relationships between plastic .axial strain and octahedral stress ratio f'or untreated granular materials

82

granular layers computed by the linear layered elastic program do not

truly represent realistic field conditions. The author also believes

that eventually the granular particles start to move, and since energy

is dissipated during the movement, the stress intensities may be sub­

stantially changed as compared to those during the stress buildup stage.

Since the magnitude of vertical compressive stress under a wheel load

depends upon the magnitude of confining pressure in granular materials,

the magnitude of vertical compressive stress cr1 in a pavement structure

may not be a constant but rather will vary during the loading process.

Also, since aircraft loadings are not always applied at one point but

vary laterally with respect to the center line of the runway, it is

likely that material in a pavement may move in directions other than

the vertical when the load is not directly over the point where the

material is located. It can be concluded that (a) the states of stress

existing in the granular layers under aircraft loadings are extremely

complicated, which cannot be simply described by constant values of

vertical compressive stress cr1 and horizontal stress cr3

, which are.

computed by the layered elastic program; and (b) the response of the

granular materials to the repeated applications of aircraft loads cannot

be simulated by the laboratory repeated load triaxial tests.

A nonlinear finite element program which incorporates the stress­

dependent moduli of granular materials was also used to compute the

stress states in the granular l~er. Compressive radial stresses were

computed in many cases, but the magnitudes were very small; i.e.,

1/2 to 1 psi. The octahedral stress ratios computed at the bottom of

the granular layer were generally two. However, extrapolations beyond

the confidence level still had to be used to estimate the permanent

strains (see Figure 22).

It should be pointed out that although layered elastic program

predicts radial stresses incorrectly, the presence of radial tensile

stresses in granular layers does not seem to affect the predictions of

vertical stresses and deflections appreciably. Reference 55 presents the

results of comparisons of computed and measured stresses and deflections.

A nonlinear finite element program was used to compute stresses and

deflections in a prototype test section constructed at WES and the com­

puted values were compared with instrumentation values. The comparisons

were favorable.

It can be concluded that the response of granular materials to

repeated applications of aircraft loads in an actual runway are extremely

complicated and are not fUlly understood. The stress states in the

granular layers cannot be accurately predicted using existing computer

programs. For design purposes to minimize the potential of permanent

deformation in untreated granular materials, it may be the best, at

least at the present time, to specify strict compaction requirements

and select materials with higher modulus values.

Fine-Grained Subgrade Soil. Since vertical subgrade strains have

been used in rational pavement design as a means to insure that permanent

deformation in the subgrade does not lead to excessive rutting at the

pavement surface, relationships between the computed vertical strains at

subgrade surface and coverage levels for all the pavements analyzed were

included in the figures which show permanent subgrade deformations

(Figures 23, 26, and 27).

Stress Factor. The concept of a stress factor was explored in

this study to estimate the potential of permanent deformation in sub­

grade soils. As shown in Equation 10, permanent strain in the subgrade

soil is proportional to the applied stress state. (It is the deviator

stress in this case.) When the deviator stresses in the subgrade along

the vertical depth are increased or decreased, it is anticipated that

the permanent deformation will also be increased or decreased accord­

ingly, Therefore, the computed deviator stresses along the vertical

depth of the subgrade soil of a pavement may be used as an indirect

measurement of the potential permanent deformations in the subgrade.

The term stress factor is defined in this report as the summation of

·deviator stresses along the vertical depth of the subgrade, which can

be computed as the sum of the products of the deviator stress computed

at various points in the subgrade and the thickness of the corresponding

sublayer. The stress factor is expressed in units of pounds per inch.

84

It will be seen later that the stress factor is very useful in discussing

the differences in stress conditions in pavements under single- and

multiple-wheel loads.

The following example illustrates the computation of a stress

factor in the subgrade of a pavement. The procedure is shown in

Table 9 and the stress factor computed is 1580.9 lb/in. It should be

pointed out that for a given pavement under a given wheel load the

stress factor is always a constant, but the accumulated permanent

deformation in the subgrade always increases as the number of load

repetitions increase.

Multiple-Wheel Heavy Gear Load (MWHGL) Tests. The relationships

between the computed values of vertical strains, permanent deformations,

and stress factors in the subgrade and the coverages at failure of the

11 MWHGL test pavements are shown in Figures 23a-23c, respectively.

Information on the 11 pavements is shown in Table 8. Because of the

special subgrade condition in pavements 2 and 6, the computed values of

these two pavements deviated from pavements 1 and 5, respectively.

Straight lines shown in Figures 23a-23c were drawn through data points

without considering pavements 2 and 6. The significances of the com­

puted values of ·the$e two pavements are discussed separately.

Figure 23a indicates that good correlation exists between the

subgrade vertical strains and the coverage levels, indicating that

subgrade strain is a good parameter to correlate pavement performance.

Of special interest is the fact that strain values shown in Figure 23a

are very close to those. developed by The Asphalt Institute and shown

in Table 2. Figure 23b shows permanent deformations computed at the

failure coverage for the 11 test pavements. Figure 23b also shows

that the computed subgrade deformations for the test pavements are

independent of the coverages by a given type of wheel configuration and

load; however, the deformations are different for the two types of wheel

configuration and load. For the C-5A loading, a subgrade permanent

deformatimf approximately 0.2 in. (computed) failed the pavement.

In Figure 23b, the measured magnitudes of upheavals, maximum permanent

surface deformations, and pavement thicknesses for each test pavement

Table 9

Computation of a Stress Factor

Depth* Thickness Deviator Stress**

in. of Layer, in. crl - cr3 ' psi Deviator Stress x Thickness

5 10 23.68 236.8

15 10 17.91 179.1

25 10 13.96 139.6

40 20 10.06 201.2

6o 20 6.95 139.0

8o 20 5.91 118.2

115 50 3.63 181.5

165 50 2.09 104.5

240 100 1.11 111.0

340 100 0.64 64.0

440 100 0.46 46.0

590 200 0.30 60.0

Sum = 1580.9 lb/in.

* The depth is measured from the subgrade surface. ** The stress is computed at the midpoint of the layers.

86

():) ~

" >

"" z. -z <-a:' 1-" (/)~ ...J.., c(• ~Q 1-D: w >

z " ll.

1-<J zz ~0 c(-~I-D:c( w~ o..D:

0 I&.. w 0

.. a: 0 1-U· c(~ I&..' (I)ID en ...I w a: 1-en

5

4

3

2

0.1

500

0

X

7 LEGEND c -Xx;.,._

9 BOEING 747 1 TWIN-1ANDEM, 240 KIPS C-5A 1 12 WHEELS_, 360KIPS

10 100 I.

5

~-x-6 II

IPOO

NOTE: NUMBERS IN PARENTHESES INDICATE MAXIMUM SURFACE PERMANENT DEFORMATION, UPHEAVAL, AND TOTAL PAVEMENT THICKNESS,RESPECTIVELY, MEASURED IN INCHES. •

02(2.4,1.0,33) 03(3.5,a7,41} 'UPHEAVAL

ol(2.4,o9,33) x6(l3, o.5,33}

7(.2 9 0 8 15i} I0(2·3·1. 2, 24) 5'1. 8 0 7. 331 ----------------XX . , . ' X X X ( .. ' • ' '/ x4(/.8,l8,15) 9(0.5,0.4,24) 8(2.8,0.4,1.5) Xll(l.8,1.1,24)

10 100 IPOO b .

~ ~ 4 2 XX7 X8 X 10 5 -x - "~~~-x-

- 6~ II

10 100 COVERAGES AT FAILURE

c.

tpoo

10,000

10,000

10,000

Figure 23. Relationship between vertical strain at subgrade surface, permanent deformation in the subgrade, and stress factor in the subgrade and performance of pavement under single-wheel loads

are given in parentheses by the pavement numbers. It can be seen that

for all pavements the measured surface deformations or ruttings were much

greater than computed subgrade ruttings. It is interesting to note that

surface ruttings for pavements with thick AC layers (pavements 7, 8, 10,

and 11*) were much greater than those for the corresponding conventional

flexible pavements. The large ruts must have been caused by the hot

temperatures during the traffic period. The asphalt contents of these

pavements are shown in Table 10. 'Since pavement 4 was failed by less

than 10 coverages, the measured surface rutting and upheaval were con­

sidered to be unreliable and are thus discarded in the subsequent

discussions. For conventional flexible pavements (i.e., pavements 1

and 3 for the Boeing 747 and pavements 9 and 5 for C-5A), it can be

seen that the measured surface ruts are not constant but increase as

the pavement thickness increases. At a given performance level, say

280 coverages, the measured surface rutting of the thicker pavement

needed for the heavier load** (Boeing 747) was greater than that of

the thinner pavement required for the lighter load (C-5A). This

observation is of vital significance in design for the prevention of

pavement rutting, and will be discussed further. Similar results were

also noted for test sections containing stabilized layers; the measured

surface ruttings are tabulated in Table 11. Each test section was con­

structed with sufficient width to conduct traffic tests with different

*

**

Although the total load of the C-5A assembly (360 kips) is heavier than that of the Boeing 747 twin-tandem assembly (240 kips), the load per wheel for the C-5A (30 kips) is much lighter than that of the Boeing 747 (60 kips), and the gear configurations (Figure 21) are such that the load is more concentrated for the Boeing 747 than for the C-5A and thus induces more rutting in the pavement.

Since the measured permanent deformation in pavement 11 (24-in. AC layer) was much less than that measured in other deep asphalt pave­ments (pavements 7, 8, and 10), it leads to the belief that the majority of rutting in a deep AC pavement occurs in the upper portion and the subgrade soil is well protected from rutting under the thick AC layer.

88

Pavement No.*

8

1

11

10

Table 10

Asphalt Contents in the Full-Depth AC Pavements

Top 3 in.

AC surface 3 to 15 in. course (4.5 percent asphalt)

3 to 9 in.

9 to 15 in.

3 to 9 in.

9 to 24 in.

3 to 9 in.

9 to 24 in.

Other Layers

Bituminous stabilized base course gravelly sand with 6.5 percent cement filler (2.9 percent asphalt)

Surface mix (5.0 percent asphalt) base course Surface mix (2.9 percent asphalt) base course

Surface mix (5.0 percent asphalt) base course Bituminous stabilized gravelly sand subbase (2.9 percent asphalt)

Surface mix (5.0 percent asphalt) base course Unstabilized gravelly sand subbase

* Numbers refer to pavement number in Table 8.

89

\0 0

Pave-r:ent :i:l. la

lh

<a

2b

3a

3b .. 4b -5•

5b

5c

6a

cb ~.

Ta

7b

Tc

Aircraft ~e

Boeing 747

Boeine74T

I Boeir.g 747

I Doeing 747

Boeir;g 747

I Boeing 747

Eoeing 747

~oeing 747 1

I C-5!. !2 W:"l.eels,

Eceir.g 747

Sir.gle

C-5A 12 'o'heels

~oeirig 74T

$i:;,~lP.

C-5f.. 12 l.'heelo

Eoeing 74T

Sir.gle

Assembly Thickneu nt Load Surface kios Course in.

200 3

24C 3

200 3

240 3

200 3

240 3

200 3

240 3

360 3

160 3

50 3

3oo 3

160 3

50 3

36o 3

16o 3

T5 3

Table 11

Measured Surface Rutti!llll in Pnelllellte vi tb stabilized Layers

Pavement Deocrintion Thiel<.neiB StAbilizilll Thlckneaa Stabilizilll

1'1. l'.aterial .kent in. Material ARent

6 Crushed - 2~ Lean 3 percent Stone ~lq lime

2 percent port lend cement

10 percent tly ash

Same as la

- - - 25 Lean 5 percent clq portland

ceaent

Some aa 2a

25 Gravelly 5 percent -- - -Sand portland

cement

Some ae 3a

25 Clayey 5 ~ercent - - --Sand portland

ceent

Same as La

6 Crushed -- J 15 Lean 3.5 .per-Stone clay cent lille

Same aa 5a

Sa.rae as 5a

6 Crushed - I 15 Lean 10 percent Stone clq portland

e•ent S..:e aa 6a

' ,......, aa..:, '

l 2l Clayey rl6 ~ercent - - -Gravelly portland Sand cement

Saroe ae Ta

Sue aa T~

Meaaured Mex1- Degree ,..., Deforu- or Coveragea

Subgrade tion at Pav.,.ent to CBR Fai~ure in. Cracki!Ut Fail'J!'e

-5.6 1.2 Severe 3,€60

~.~ 3.2 Severe 6?0

5.~ 1.1 Severe 3,660

•• 0 l.k Severe :!laO

3.8 1.5 Severe T ,820

3.2 2.5 Slight ~20

4.9 O.T Severe 1,3SO

5.2 l.T Severe 120

5.0 0.96 Severe 118

5.0 0.96 Severe 140

5.0 0.6 Severe Lo

L.3 l.o8 SeYere 1,200

L.3 1.8 Severe 1,000

h,3 l.n Severe ~0 --L.3 0,84 Slight llo hil-

ure &t 10,1)00

~.2 1.32 Severe 1,810

~.2 0,8 Senre 120

--

gear assemblies. It can be seen that for the same pavements, which the

sections trafficked by heavier load failed earlier, the measured surface

ruts were greater than those failed by lighter loads. Table 11 also

shows that under a given load assembly, the measured surface ruts in­

crease with increasing coverages. The relationships are plotted in

Figure 24. In other words, two different pavements failed by a given

assembly load at different coverage levels can experience different

degrees of surface rutting, with greater rutting measured in stronger

pavements.

Permanent deformations computed for pavements 2 and 6 were sub­

stantially greater than those for pavements 1 and 5, respectively. This

is because of the existence of the extra-weak l~er in pavements 2 and 6. It should be reiterated that the existence of a deep soft layer in the

pavement was observed to have no significant effect on overall performance.

Figure 23c shows the computed stress factors for the 11 test pave­

ments. The stress factor decreases with increasing coverages (or in­

creasing thickness of the pavement). However, different aircraft loads

result in different relationships between the stress factor and the

number of coverages, while the relationships shown by the straight lines

are parallel to each other. The reason for the larger stress factors

in pavements subjected to the Boeing 747 load is the closer spacing of

the wheels and the heavier load for each wheel (consequently, the

stresses in the subgrade were more concentrated). The stress factors

computed for pavements 2 and 6 were slightly smaller than those for

pavements 1 and 5 because of the existence of the extra-weak layer in

the pavements.

The computed permanent deformations shown in Figure 23b are

maximum values under the assembly loads. Since pavement performance also

depends on deformations at offset points, attempts were made to compare

the deformation basins of several pavements designed for Boeing 747 and

C-5A loadings at th~ same coverage levels. The thicknesses of these

conventional flexible pavements were determined by the subgrade vertical

strain criterion shown in Figure 23a. A trial-and-error procedure was

used to determine the correct thicknesses of pavements constructed on

91

f\C) 1\)

4 I

LEGEND

t~ • BOEING 747, 240 KIPS 0 BOEING 747, 200 KIPS

NOTE: NUMBERS BY SYMBOLS ARE TEST

~ NUMBERS FROM TABLE H ~ a:: 0

e3b L&. LLI 0

LLI 2 u ~ •"b L&. a:: ::::>

/ .2b (/)

0 LLI a:: ::::> (/)

~ LLI ~

0 1 I I I I I I I I I I I I I I I I II . I I I I I I I 11 I I I I I I Ill I 10 100 1,000 10,000

COVERAGE AT FAILURE

Figure 24. Measured surface permanent deformations of test pavements at time of failure, pavements with stabilized layers

4-CBR subgrade soil in which the computed vertical strains at the subgrade

surface were 2.7 x 10-3 and 1.9 x 10-3 in./in. for pavements designed at

coverage levels of 100 and 1000, respectively. Permanent deformations at

offset points of these pavements were computed and the deformation basins

are presented in Figure 25. While the maximum deformations are nearly

the same, the deformation basins for thicker pavements are flatter than

those of the thinner ones. The flatter basin naturally would cause less

shearing deformation in the overlying pavement layers and contribute to

better performance. On the other hand, the sharper deformation basin

in the subgrade soil of thinner pavements causes more severe shearing

deformation in the pavement layers and contributes to surface layer

cracking and earlier failure of the pavement. Explaining it in another

manner, the better performance of thicker pavements, besides many other

reasons, is due to not only its greater structural capacity, but also

the flatter deformation basin in the supporting subgrade soil.

Attempts were made to compare the deformation basins of the

Boeing 747 and C-5A gear assemblies. It was difficult to select basins

which were comparable since the wheel configurations are very different.

However, it can be readily seen that under the C-5A load the maximum

deformation is smaller and the basin is flatter and broader because the

assembly has more wheels and they are spaced much farther apart. Con­

sequently, pavements designed for C-5A loadings at the same coverage

levels as for Boeing 747.loadings require much less thickness. For

instance, for pavements designed for 1000 coverages, a 48.5-in.-thick

pavement is required for the Boeing 747 but only a 29.6-in.-thick

pavement is required for the C-5A.

The subgrade permanent deformations presented in Figure 23b are

computed values. Measured deformations from open trench tests were

available for several test pavements. Comparisons between measured and

computed deformations are presented in Figure 26. If the computed values

are the same as the measured ones, the points should be plotted on the

1:1 line. Although the measured values from open trench tests are not

very accurate, the results presented in Figure 26 indicate that the

computed values are much smaller than the measured ones. Although the

93

... a..

<J z 0

~ ~ a:

OFFSET, IN.

0o~----~2~o ______ 4~or-----~6o ______ _,-------.--------x

y

C-5A, 12 WHEELS, 360KIPS

f=221N. IOOCOVERAGES

t = 29.6 IN. 1000 COVERA,.GES

26.5"

a.

X..,........

~ 00 0000

I 0'0

-eeleo .. x ~ ~26.5" --1 ~ 60.5"

f2 OFFSET, IN.

~ 0o~----~2To~-----4;0~----~6rO------~~-----.r-----~x ..... z w z < ~ f5 0.1 a

0.2

y

8-747 1 TWIN-TANDEM - 240 KIPS

22"

t =.16.31N. 100 COVERAGES

t = 48.5 IN. 1000 COVERAGES

b.

58"[010 6•0 "'X

~ 1--- 22"

Figure 25. Subgrade permanent deformation basins in pavements

0.5

,0.4 s::

•r-i

o.r

0 0 0.1 0.2

·' ,. ~

,~ 'v

o B~747, Twin-Tandem 240 kips

b. C:-5A, 12 Hheels 360 kips

Q.3

Compl.lted Deform3.t ion, in.

Figure 26. Comparisons of measured and computed subgrade permanent deformations

95

measured values are greater than those computed, the conclusions derived

from those in Figure 23 still hold. For instance, Figure 23b shows that

the computed subgrade deformations for the Boeing 747 (240 kips) are

greater than those for the C-5A (360 kips).* It was concluded that, at

a given coverage level, subgrade deformations are greater for pavements

designed for heavier loads. Figure 26 shows that the difference in the

actual subgrade deformations between heavier and lighter loads could

even be greater than the computed values presented in Figure 23b.

Single-Wheel Loads.. Analyses were made on test pavements failed

by single-wheel loads. The test pavements had various thicknesses and

were constructed'on subgrade soils with CBR's ranging from 4 to 18.

The pavements failed at different coverage levels under loads ranging

from 10 to 200 kips. Pavement information can be found in Table 1 of

Reference 51. Repeated load test data from the second series of tests

(Figures 17a-17e) were used in the analysis. The accumulated permanent

deformations· occurring in the subgrade of the pavement seemed to vary

with the thicknesses of the pavement, wheel load, and subgrade CBR.

Because the laboratory test data were inconsistent, as was explained

earlier, and also because of the limited number of test pavements and the

relatively significant number of variables, the relationships between the

variables cannot be used as the basis for a meaningful analysis. Labora­

tory data from the first test series could not be used to analyze the

single-wheel loads because of the limited range of CBR's. In this report,

only an analysis of pavements designed by the CBR equation at lower sub­

grade CBR's is presented.

Formulation of the CBR equation56 was based on results of numerous

full-scale accelerated traffic tests, which represented reliable data

and extensive observations of the Corps of Engineers. A pavement designed

by the CBR equation has a thickness sufficient to prevent shear failure

in the subgrade soil. The equation has the form

* The Boeing 747 (240 kips) is considered to be heavier than the C-5A (360 kips). The explanation can be found in the footnote on page 86.

~ p A t = a B.l CBR - ; (12)

in which P is the wheel load in pounds, A is the tire contact area

in square inches, a is a factor depending upon the selected coverage

level, and t is the total thickness in inches, including the AC and

granular base layers. The thicknesses of AC and base layers were

determined by Corps of Engineers standard flexible pavement design

procedure.

Many pavements were designed by the CBR equation for 5000 cov­

erages and for various loads and subgrade strengths. Elastic vertical

strains and deviator stresses were computed by the elastic layered 46

program, and permanent deformations at the subgrade surface were

computed by Equation 11. The results are presented in Figure 27. It

can be seen that for pavements designed for same coverage level, the

elastic vertical strain at the subgrade surface (Figure 27a) increases

slightly with an increase in the subgrade CBR. At a given subgrade CBR,

the subgrade strain also varies slightly with the load, with larger

strains induced by greater loads. For subgrade CBR ranging from 2.4 to

6 . -3 8 -3 I .3, the average strain increase was from 1.5 x 10 to 1. x 10 in. in.

For practical de~ign purposes, it can be assumed that subgrade strain is

independent of the load. This becomes clear when these strain values are

used to determine coverage values from the relationship between strain

and coverage at failure shown in Figure 23a.

The computed deviator stresses at the subgrade surface of these

pavements are presented in Figure 27b. It can be seen that for pavements

designed for the same coverage level, the deviator stress at the subgrade

surface increases nearly linearly with an increase in the subgrade CBR,

but is nearly independent of the magnitude of the wheel load. The lack

of dependence of the deviator stress on the magnitude of the wheel load

is reasonable because these pavements Jere designed by the CBR equation

and therefore an adequate thickness of pavement was provided to protect

the subgrade from shear failure. For pavements constructed over a sub­

grade having the same CBR, the stresses of the subgrade surface should

be the same for any design wheel load.

97

~ 2.0 <( • o::Z 1--::::. C/) • 1.8

z J­<( u '? 1.6 -o 1--0:: w >

Cl) 20 0. .. Cl) 15 C/) w 0:: 1-C/)

0:: 0 ~ >

02 w 0

~ 0.3 ... 0.

<3 z 0

~ 0.2 :e 0:: 0 "-w 0 1- 0.1 z w z c( :::!: 0::

~ 02

Figure 27.

3 4

3 4

5000 DESIGNED COVERAGES

a

5

b

3 4 5

6 .,

6 7

LEGEND INFLATION PRESSURE

PSI LOAD KIPS

10 30 30 60 60

6

100 100 300 100 210

1 SUBGRADE CBR

c.

Relationships between elastic vertical strain and deviator stress at subgrade surface and permanent deforma­tion in the subgrade for pavements designed at 5000 cov­erages for many single-wheel loads

Figure 27c indicates that, for pavements designed for the same

coverage level, the subgrade permanent deformation .decreases with in­

creasing subgrade CBR and with decreasing wheel load. This effect may

be explained as follows. Laboratory repeated load test results shown

in Figure 18 indicate that at the same load repetition level the permanent

strains of subgrade soils with higher CBR's are much smaller than those

with lower CBR's. Although the stress intensity in subgrades with higher

CBR's is larger, which tends to increase the permanent deformation (Fig­

ure 27c), the decrease in permanent deformation because of the stronger

soil exceeds the increase due to the higher stress intensity. Conse­

quently, the permanent deformation decreases with an increase in the

subgrade CBR. At. a given subgrade CBR, larger wheel loads induce larger

stress intensities in the subgrade and thus cause larger permanent

deformations. It should be noted that the deviator stresses shown in

Figure 27b are stresses on the subgrade surface; however, it is the

stresses along the vertical depth in the subgrade (i.e., the stress

factor) which govern the total permanent deformation in the subgrade.

The analysis presented in Figure 27 is for pavements designed

at 5000 coverage levels. Analyses were also made on pavements designed

at different coverage levels. The relationships between the computed

values of vertical subgrade strains, permanent deformations, and stress

factors in the subgrade and the designed coverage levels of three pave­

ments are shown in Figure 28a-28c, respectively. It can be seen that

good correlations exist b~tween the three parameters and t.he design cov­

erage levels. It should be noted, however, that permanent deformation

occurring in the subgrade decreases with increasing designed coverage

levels, which is a different response from that under multiple-wheel

loads (Figure 23b) in which the permanent deformations under one given

type of aircraft load were nearly the same for all the coverage levels

within the test range. The difference may lie in the differences in

stress intensities occurring in the subgrade soils between single and

multiple wl1eels. The difference may be explained by the stress factors.

Figure 29 shows a comparison of relationship between the stress

factors and coverages at failure for single- and multiple-wheel loads

99

"' > w z -z <C-a:' .._. . (/)~

_Jfl) <(, uo --.._. a: w >

i

"' 0. r-<l zz ~0 <(-~.._. a:<( w~ a.. a:

0 1.&.. w 0

" a: 0 .._. u <(' IL~

' (f)ID (/).J w a: .._. (/)

1.0 200 1,000 10,000 50,000

a. 60 KIPS (2~0-PSI INFLATION

! PRESSURE)

t 41N.AC

1 GRANULAR LA~6p

•

0.1

0.04 200 1,000 10,000

b.

300 200 t,ooo 10,000

COVERAGES AT FAILURE c.

Figure 28. Relationships between vertical strain at the subgrade surface, permanent deformation in the subgrade, and stress factor in the subgrade and performance of a pavement under single-wheel loads

100

50,000

50,000

I-' .Q I-'

3000 z '2000 co ...J

a: 0 t­u < IJ..

(f) (f) w 0::: t­CI)

-

C-SA LIN£ FROM FIG. 23 C

SINGLE-WHEEL LINE FROM FIG, 27C

100 1000 5000

COVERAGES AT FAILURE

Figure 29. Comparison of stress factors for single- and multiple-wheel loads

(the curves were taken from Figures 23c and 28c). It can be seen that

the rate of decrease in the stress factor with increasing pavement

thickness (or increasing coverages) for single wheels is much greater

than that for multiple wheels. Laboratory repeated load test results

shown in Figures 16 and 17 indicate that, while the permanent strain

increases slightly with increasing load repetitions, it decreases

rapidly with decreasing stress intensity. With the steep slope of this

curve (in Figure 28) for single-wheel loads, the decrease in permanent

deformation due to reduction in stress intensities with increase in

thickness exceeded the increase in permanent deformation because of

higher repetition levels. Therefore, the accumulated permanent deforma­

tion occurring in the subgrade of pavements under single-wheel loads

decreases with increasing coverages. With the gentle slope of the line

shown in Figure 29 for multiple-wheel loads, the decrease of pavement

deformation~ due to reduction in stress intensities, may equally offset

the increase because of higher repetition levels. Therefore, the

accumulated permanent subgrade deformations under multiple-wheel loads

become nearly the same for all coverage levels.

Permanent deformations were computed at offset points for the

three pavement thicknesses shown in Figure 28 and the deformation basins

are shown in Figure 30. It should be noted that as the thickness of the

pavement increases (or the coverage level increases), not only is the

maximum deformation reduced, but the curvature of the deformation basin

is also reduced. This, of course, reduces shearing deformations in the

overlying pavement structure and contributes to better performance of the

pavement. On the other hand, a thinner pavement under the same wheel

load has a sharper curvature of the deformation basin in the subgrade

than the surface and induces larger shearing deformation in the overlying

pavement layer. This definitely causes surface layer cracking and con­

tributes to earlier failure of the pavement.

102

z 00

... a.

<]

z 0 ..... 0.1 4: ~ a: 0 LL. w 0 0.2 ..... z w z 4: ~ a: 0.3 w (l.

OFFSET, IN. 10 20 30 40

T=35.8 IN. 5000 COVERAGES

/000 COVERAGES

200 COVERAGES

60 KIPS (210-PSI INFLATION PRESSURE)

5.4 CBR

Figure 30. Permanent deformation basins in pavements designed at various coverage levels under single-wheel loads

],03

DESIGN IMPLICATIONS OF COMPUTED RESULTS

Because computations of permanent deformation in AC and untreated

granular materials could not be made in this study, discussion on their

design implications has been om.i tted in this section. Computations of

permanent deformations were only made for fine-grained subgrade soils in

pavement systems. Although the deformation characteristics of subgrade

soil alone cannot fully describe the overall deformation behavior of the

pavement, the findings can certainly shed light on the design concept

of flexible airport pavements. They are discussed in the following

paragraphs.

The difference in the rate of decrease in the stress factor with

an increase in pavement thickness between single- and multiple-wheel

loads shown in Figure 28 indicates that, as the design pavement service

life is increased, the need for an increase in pavement thickness to

reduce the stress intensity in the subgrade for multiple-wheel loads

is less than that for single-wheel loads. This difference in requirements

conforms with present Corps of Engineers and FAA design criteria in which

the thickness adjustment factor a is smaller for multiple-wheel loads

than for single-wheel loads. (Details of the development of the design

criteria can be found in Reference 51, Volume I, with reference to

Figure 69.)

The analysis indicates that pavement performance can be predicted

much easier by the resilient vertical strain at the subgrade surface than

by accumulated subgrade permanent deformation. Unlike the resilient

vertical strain, the accumulated permanent deformation in the subgrade

was found to be dependent on many factors: load, gear configuration,

pavement thickness, subgrade strength, subgrade condition, and coverage

level. They are discussed separately as follows:

a. Load. Figure 23b indicates that the computed accumulated permanent deformations of the Boeing 747 240-kip assembly load were much greater than those of the C-5A 360-kip assembly load. The analysis of single-wheel loads shown in Figure 27c also shows that, for pavements designed for the same perform­ance level, the permanent subgrade deformation increases with an increase in wheel load, with the increase being more pronounced for pavements on weaker subgrades.

104

*

b. Gear configuration. The main differences in the gear con­figurations of the C-5A 12-wheel assembly and the Boeing 747 twin-tandem assembly are that C-5A has more wheels and the wheels are much farther apart. Pavements 1 and 5 had identical thicknesses and subgrade strengths, but the failure coverage levels of these two pavements subjected to C-5A and Boeing 747 assembly loads were 1500 and 40, respectively. A comparison of the deformation basins of the C-5A (Figure 26a) and the Boeing 747 (Figure 26b) indicates that, for pavements designed for the same performance level, the maximum deformations in the subgrade of pavements designed for C-5A are not only much smaller, but the basins are much flatter and broader.

c. Pavement thickness. In Figure 23b, the accumulated subgrade deformations computed for the Boeing 747 were much greater than those computed for the C-5A. It should be noted that for the same performance level, the Boeing 747 requires a much thicker pavement than the C-5A. It can be stated that for pavements designed for the same performance level, heavier loads* require thicker pavements and thicker pavements can withstand larger subgrade deformations. This fact is well illustrated by the deformation basins plotted in Figure 25. As shown, for the two pavements designed for the 1000 cov­erage level, the required pavement thickness is 29.6 in. for the C-5A, but is 48.5 in. for the Boeing 747. The deformations in the pavement under the heavier load (Boeing 747) were not only much greater but the deformation basin was also much sharper than that under the lighter load (C-5A).

d. Subgrade strength. Figure 27c shows that the permanent sub­grade deformation decreases with increasing subgrade CBR for all the single-wheel loads. The pavements were designed using the CBR equation for a coverage level of 5000. For multiple­wheel loads, although an analysis was not performed on pave­ments with subgrade CBR's higher than 4, it is believed that permanent subgrade deformation would also decrease with increasing subgrade CBR. This behavior occurs because a stronger subgrade requires a thinner pavement and a thinner pavement is followed by lower subgrade permanent deformation as was discussed in the previous paragraphs.

e. Subgrade condition. The difference between pavements 1 and 2 and pavements 5 and 6 is that an extra-weak layer (3 ft) was placed deep in the subgrade of pavements 2 and 6. Figure 23b shows that the permanent subgrade deformations in pavements 2 and 6 were much larger than those in pavements 1 and 5, respec­tively, while the overall performance of pavements 1 and 2

Heavier load refers to load per wheel and closer gear spacings. information can be found in the footnote on page 86.

~05

More

f.

and pavements 5 and 6 were the same. Apparently, the soft layer deep in the subgrade deformed nearly uniformly under the action of the multiple-wheel loads. Consequently, the pave­ment structure above the soft layer moved downward nearly uniformly following the movement of the soft layer without experiencing any significant additional bending stresses as compared with those in pavements 1 and 5 in which the soft layer did not exist.

Coverage level. An analysis made on pavements designed using the CBR equation for single-wheel loads (Figure 28b) revealed that the accumulated permanent subgrade deformation decreased as the performance level of the pavement increased. In other words, the permanent subgrade deformation of a pavement de­signed for a higher coverage level is less than that of a pavement designed for a lower coverage level. However, an analysis of pavements failed under multiple-wheel loads revealed that under a given aircraft load pavements of dif­ferent thicknesses failed under different coverage levels but experienced nearly the same amount of computed permanent subgrade deformation (Figure 23b). This is due possibly to the differences between single- and multiple-wheel stress distributions in the subgrade. These results are reasonable because the laboratory repeated load test results shown in Figure 19 indicate that for a given value of elastic strain the permanent strain in the subgrade increases with decreasing CBR values. This relationship also explains why, for pave­ments designed using the CBR equation for 5000 coverages, permanent strain increased with decreasing subgrade CBR's (shown in Figure 27c), while the subgrade elastic strains were nearly the same (Figure 27a).

Prior to further discussion, the current concept and practice in

considering pavement rutting in flexible pavements should be reviewed,

and the measurements of surface deformations obtained from field test

pavements should be investigated. The conclusions can thus be compared

with the results of this study.

As was stated in the beginning of this report, one of the current

approaches to consider pavement rutting under repeated traffic loading is

to limit the vertical compressive strain at the subgrade surface to some

~olerable amount associated with a specific number of load repetitions

(e.g., limiting subgrade strains in Table 2). By controlling the charac­

teristics of the materials in the pavement section through materials

design and proper construction procedures (unit weight or relative com­

paction requirements) and by insuring that materials of adequate stiffness

106

and sufficient thickness are used so that the strain level is not exceeded,

permanent deformation can be limited to a value equal to or less than the

prescribed amount. It should be reiterated that in the Corps of Engineers

failure criteria, from which failure coverages of field test pavements

were determined, surface rutting is not considered to be a critical

factor in judging pavement failure. The criteria were described on

page 75 of the report. Consequently, surface rutting measured at

failure in the field test pavements constructed and tested at WES was

not constant but varied with pavement thickness and gear loads. It was

found that at a given performance level, the measured surface rutting

increased with increasing pavement thickness. The need for thicker pave­

ments may be due to either heavier loads or softer subgrade soils (see

Figure 23b). Since the limiting subgrade strain criteria developed by

The Asphalt Institute (shown in Table 2) were based in part on an analysis

of Corps of Engineers test data, 50 it is evident that the criterion of

surface rut depth is not included in the developed performance models.

Although the criteria developed by She1120

(Table 2) were developed using

elastic analysis of pavements designed according to the CBR procedure

and performance results of the AASHO Road Test, the criteria are thought

to be associated with ultimate rut depths on the order of 3/4 in.

Limiting surface rutting is a concept that has been advocated in recent

years; however, it has not yet been implemented in any existing design

procedure.

The discussions presented in this report are in direct contrast

with the generally accepted concept which assumes that if the material

and thickness of a pavement are properly selected and proper compaction

is applied so that the elastic subgrade strain is limited, subgrade

rutting will be controlled and surface rutting equal to or less than

some prescribed amount can be assured. This concept is based on the

assumption that when two pavements are designed for the same performance

level (same coverage at failure), not only are the subgrade elastic

strains the same but also the subgrade rutting is very nearly the same.

This assumption is not strictly correct based on the results of the

analysis in this study.

107

It is the author's belief that the surface rut depth measured at

the time when the pavement is judged to be failed increases as the thick­

ness of the pavement is increased, even though the material in each layer

of the pavement may be properly selected and compacted. Since surface

rut depth is not limited in the failure criteria, when two pavements are

designed for the same performance level, the surface rut depth and sub­

grade rutting will be greater for the thicker pavement (greater thick­

ness due to either heavier applied loads or weaker subgrade support),

while the elastic vertical strain at the surface of the subgrade will

be nearly the same for the two pavements.

If it is desirable that pavements designed for the same performance

level have the same degree of rutting in the subgrade, the elastic verti­

cal strains at the subgrade surface induced by the load will have to be

varied, with smaller elastic strains allowed for weaker subgrades and

greater elastic strains allowed for stronger subgrades in accordance with

the relationships between the elastic and permanent strains shown in

Figure 19. This is, of course, in contrast with the current limiting

subgrade strain criteria concept in which pavements designed for the

same performance level have the same elastic vertical strains at the

subgrade surface. The limiting subgrade strains for both highway and

airport pavements adopted by a number of agencies are shown in Table 2.

l08

CONCLUSIONS AND RECOMMENDATIONS

CONCLUSIONS

Based on the material from the literature survey and results of

analysis of full-scale test pavements and pavements designed using the

CBR equation, the following conclusions were drawn. A linear layered

elastic computer program was used to compute the permanent deformations

in granular layers and in the subgrade soils, with the material charac­

terizations described in the section LABORATORY REPEATED LOAD TESTS.

Therefore, the computed results are subjected to the criticism of the

computer program as well as the material characterization.

a. AC surfacing. There is no general consensus on the method with which the permanent deformation of an AC layer in a pavement system can be computed. Laboratory tests to deter­mine the rutting properties of AC are expensive and time-conswning.

b. Untreated granular layers. A serious problem exists in the prediction of permanent deformations in untreated granular layers in a pavement system. The stress states in the granular layers under the aircraft loadings cannot be com­puted correctly using Burmister layered elastic solution and the nonlinear finite element program in its present form. Also, the stress states under aircraft loadings cannot be correctly simulated by laboratory tests.

c. An analysis made on the computed permanent deformations occurring in the subgrade soil of many full-scale test pave­ments and pavements designed using the CBR equation indicates that the current concept of controlling subgrade rutting through limiting subgrade strains in flexible pavements is not strictly correct. When subgrade strains are limited, not only the subgrade rutting may not be limited, but also the control of surface rutting may not be assured. If surface rut depth is limited in design procedures, however, the limiting subgrade strain criteria proposed and adopted by many agencies (Table 2) will have to be modified to vary according to subgrade strength.

d. The approach used in tnis study was not successful in providing a prediction model to estimate the amount of permanent deformation in flexible pavements subjected to aircraft loadings.

RECOMMENDATIONS

Based on the results of analysis of this study, it is recommended

that (a) continuing efforts be made to investigate the basic deformation

characteristics of AC and untreated granular soils in a pavement system

subjected to aircraft loadings which move in a longitudinal direction

and also wander from the center line of a runway; (b) a development

program be initiated in prediction models to estimate permanent deforma­

tions in each component layer of a pavement system when the information

described in (a) becomes available; and (c) efforts be concentrated on

selecting proper component materials and speci~ing construction tech­

niques to minimize the potential of deformation, before a complete

prediction model is developed.

l;J,O

LIST OF NOMENCLATURE

The following symbols are used in this report:

A = tire contact area;

c = cohesion;

CBR = California Bearing Ratio;

D =equivalent particle size of filler (0.000004 in.);

E = modulus of elasticity;

FB = filler-bitumen factor;

LL = liquid limit;

P = wheel load;

PI = plasticity index;

q = effective deviator stress;

~t = bearing capacity;

sbit = stiffness of the bitumen;

Smix = stiffness of the asphaltic concrete mixture;

t =thickness of the pavement;

V = void factor;

y = shear strain;

o = permanent deformation; p ~Z = thickness of the sublayer;

£ = permanent strain; p

£ = maximum compressive subgrade strain; vs

d£/dt = rate of application of axial strain;

nmass = viscosity of mass;

a= normal stress;

aij = stress state;

a oct = octahedral normal stress;

a1

, a2

, a3

=major, intermediate, and minor respectively;

T = shear strength; d£1

'e = initial cohesion when dt = 0;

'oct = octahedral shear stress; and

~ = angle of internal friction.

111

principal stresses,

REFERENCES

1. Monismi th, C. L. , "Rutting Prediction in Asphalt Concrete Pavements; A State-of-the-Art," prepared for the Symposium on Predicting Rutting in Asphalt Concrete Pavements, 1976 Annual Meeting of the Transportation Research Board, Jan 1976.

2 .• Dorman, G. M. and Metcalf, C. T., "Design Curves for Flexible Pave­ments Based on Layered Sy~tems Theory," ER Record 71, 1965.

3. Yoder, E. J. and Witczak, M. W., Principles of Pavement Design,_ 2d ed., Wiley, 1975, Tables 8 and 9.

4. Barker, W. R. and Brabston, W. N., "Development of a Structural Design Procedure for Flexible Airport Pavements," Report No. FAA­RD-74-199 (WES TR S-75-17), Sep 1975, Federal Aviation Administration, Washington, D. C.

5. Hofstra, A. and Klomp, A. J. G., "Permanent Deformation of Flexible Pavements Under Simulated Road Traffic Conditions," Proceedings, Third International Conference on the structural Design of Asphalt Pavements, London, 1972, pp 613-621.

6. Heukelom, W. and Klomp, A. J. G., "Consideration of Calculated Strains at Various Depths in Connection with the Stability of Asphalt Pavements," Proceedings, Second International Conference on the Structural Design of Asphalt Pavements, University of Michigan, 1967.

7. McLean, D. B., The Measurement of Deformation Properties of As haltic Materials Under Triaxial Re eated Load Tests Ph. D. Thesis in preparation , 1973.

8. Morris, J., "The Prediction of Permanent Deformation in Asphalt Concrete Pavements," A technical report based on the author's Ph. D. Thesis, Sep 1973.

9. Monismith, C. L., "A Design Framework for Asphalt Concrete Pavements Using Available Theory," A paper used in the Institute on Flexible Pavement Design and Performance, Pennsylvania State University, Nov 1973.

10. U~ S. Army Corps of Engineers, "Flexible Airfield Pavements," TM 5-824-2, 1958, U. S. Government Printing Office, Washington, D. C.

11. California Division of Highways, "Test Method No. 304; Materials Manual_, 1, 1963.

12. Nijboer, L. W., Plasticity as a Factor in the Design of Dense Bituminous Carpets, N.Y. Elsevier Publishing Co., 1948.

112

13. Smith, W. R., "Triaxial Stability Methods for Flexible Pavement Design," Proceedings, Association of Asphalt Paving Technologists, 1949, pp 63-94.

14. McLeod, N. W., "A Rational Approach to the Design of Bituminous Paving Mixtures," Proceedingst Association of Asphalt Paving Technologists, 1950, pp 82-22 •

15. Saal, R.N. J., "Mechanics of Technical Applications of Asphalt," Preprint of Proceedings, Symposium of Fundamental Nature of Asphalt, 1960.

16. Nijboer, L. W., "Mechanical Properties of Asphalt Materials and Structural Design of Asphalt Roads," Proceedings, Highway Research Board, 1954, pp 185-200.

17. Valkering, C. P., "Effects of Multiple Wheel Systems and Horizontal Surface Loads on Pavement Structures," Proceedings, Third Interna­tional Conference on the Structural Design of Asphalt Pavements, London, 1972, pp 542-549.

18. Marais, C. P., "Tentative Mix Design Criteria for Gap-Graded Bituminous Surfacings," Jan 1974, Highway Research Board Meeting, Washington, D. C.

19. Heukelom, W. and Klomp, A. J. G., "Consideration of Calculated Strains at Various Depths in Connection with the Stability of Asphalt Pavements," Proceedings, Second International Conference on the Structural Design of Asphalt Pavements, 1967, pp 155-168.

20. Elloi tt, J. F. and Moavenzadeh, F. , "Moving Load on Viscoelastic Layered System - Phase II," Report No. R69-64, Sep 1969, Department of Civil Engineering, Materials Division, Massachusetts Institute of Technology, Cambridge, Mass.

21. Elliott, J. F. , Moavenzadeh, F. , and Findakly, H. , "Moving Load on Viscoelastic Layered Systems, Phase II - Addendum," Research Report R70-20, Apr 1970, Department of Civil Engineering, Massachusetts Institute of Technology to U. S. Department of Transportation, Federal Highway Administration, Bureau of Public Roads Under Contract No. FH-ll-6916.

22. Moavenzadeh, F. and Elliott, J. F., "A Stochastic Approach to Analysis and Design of Highway Pavements," Proceedings, Third International Conference on the Structural Design of Asphalt Pave­ments, London, 1972, pp 490-505.

23. Barksdale, R. D., "Laboratory Evaluation of Rutting in Base Course Materials," Proceedings, Third International Conference on Struc­tural Design of Asphalt Pavements, London, 1972, pp 161-174.

113

24. Romain, J. E. , "Rut Depth Prediction in Asphalt Pavements," Pro­ceedings, Third International Conference on Structural Design of Asphalt Pavements, London, 1972, pp 705-710.

25. Hills, J. F., "The Creep of Asphalt Mixes," Journal, Institute of Petroleum, Nov 1973.

26. Hills , J. F. , Brien, D. , and Van de Loo, P. J. , "The Correlation of Rutting and Creep Tests on Asphalt Mixes," Journal, Institute of Petroleum~ Paper IP 74-001, Jan 1974.

27. Van de Loo, P. J. , "Creep Testing, A Simple Tool to Judge Asphalt Mix Stability," Paper presented to the 49th Annual Meeting of the Association of Asphalt Paving Technologists, Feb 1974.

28. Snaith, M. S., Permanent Deformation Characteristics of a Dense Bitumen Macadam, Ph. D. Thesis, University of Nottingham, 1973.

29. McElvaney, J., Brown, S. F., and Pell, P. S., "Permanent Deformation of Bituminous Materials," Internal Report No. JMcE/1, May 1974, University of Nottingham.

30. Morris, J. et al., "Permanent Deformation in Asphalt Pavements Can Be Predicted," Paper presented to the 49th Annual Meeting of the Association of Asphalt Paving Technologists, Feb 1974.

31. Chompton, G. and Valayer, P. J., "Applied Rheology of Asphalt Mixes -Practical Application," Proceedings, Third International Conference on the Structural Design of Asphalt Pavements, London, 1972, pp 214-225~

32. Brown, S. F. , Pell, C. A. , and Brodrick, B. V. , "Permanent Deforma­tion of Flexible Pavements," Contract No. DAJA 73-74-1306, Nov 1974, University of Nottingham, England.

33. Brown, S. F. , "An Improved Framework for the Predict ion of Permanent Deformation in Asphaltic Layers," A paper presented at the 50th Annual Meeting of the Transportation Research Board, 1975.

34. Vander Poel, C., "A General System Describing the Viscoelastic Properties of Bitumen and Its Relation to Routine Test Data," Journal of Applied ChemistryA Vol 4, 1954, pp 221-236.

35. Van Draat, W. E. F. and·sommer, P., "Ein Gerat zur bestimmung der dynamischen elastizitat modulu von Asphalt," Strasse Autobahn 6, 1965, pp 206-211.

36. Allen, J. J., The Effects of Nonconstant Lateral Pressures on the Resilient Response of Granular Materials, Ph. D. Thesis, University of Illinois at Urbana-Champaign, May 1973.

114

37. Kalcheff, I. V., 11 Charac.teristics of Graded Aggregates as Related to Their Behavior Under Varying Loads and Envirorunents ," Presented at Conference of Graded Aggregate Base Materials in Flexible Pave­ments, Oak Brook, Ill., 25-26 Mar 1976.

38. Brown, S. F., "Repeated Load Testing of a Granular Material," Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol 100, No. GT7, Proceeding Paper 10684, Jul 1974, pp 825-841.

39. Barrett, J. R., "Modeling Permanent Strain Behavior of Unbound Base Course Materials - A Review," Technical Paper No. 26, 1976, Division of Applied Geomechanics, Commonwealth Scientific and Industrial Research Organization, Australia.

40. Finn, W. D. L., "Applications of Limit Plasticity in Soil Mechanics," Proceedings, American Society of Civil Engineers, SM-5, Part I, 1967, pp 101-120.

41. Hyde, A. F. L., Repeated Load Triaxial Testing of Soils~ Ph. D. Thesis, University of Nottingham, 1974.

42. Monismi th, C. L. , Ogawa, N. , and Freeme, C. R. , "Permanent Deforma­tion Characteristics of Subgrade Soils Due to Repeated Loading," Transportation Research Record No. 537, 1975.

43. Barker, W. R., "The Relationship Between Resilient and Permanent Strain in the Design of Airport Pavements," A paper prepared for the Symposium on Rutting in Asphaltic Concrete Pavements at the 55th Annual Meeting of the Transportation Research Board, Washington, D. C., Jan 1976.

44. Chisolm, E. E. and Townsend, F. C., "Behavioral Characteristics of Gravelly Sand and Crushed Limestone for Pavement Design, FAA-RD-75-177 (TR S-76-17), Sep 1976, U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

45. Townsend, F. C. and Chisolm, E. E., "Plastic and Resilient Prop­erties of Heavy Clay Under Repetitive Loadings," FAA-RD-76-107 (TR S-76-16), Nov 1976, U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

46. Chou, Y. T., "An Iterative Layered Elastic Computer Program for Rational Pavement Design," FAA-RD-75-226 (TR S-76-3), Feb 1976, U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

47. Kingham, R. I. and Kallas, B. F., "Laboratory Fatigue and Its Relationship to Pavement Performance," Proceedings, Third Interna­tional Conference on the Structural Design of Asphalt Pavements, 1972, Figures 6 and 7.

115

48. Witczak, M., "Design of Full-Depth Asphalt Airfield Pavements," Proceedings, Third International Conference on the Structural Design of Asphalt Pavements, University of Michigan, 1972. ·

49. Heu.kelom, W. and Foster, C. R., "Dynamic Testing of Pavements," Journal Soil Mechanics and Foundations Divisions, American Society of Civil Engineers, 1960.

50. Chou, Y. T., "Engineering Behavior of Pavement Materials: State­of-the-Art," FAA-RD-77-37 (TR S-77- ) , Chapter 6, Feb 1977 (in preparation), U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

51. Ahlvin, R. G. et al., "Multiple-Wheel Heavy Gear Load Pavement Tests," U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss., Technical Report S-71-17, Vol 1-4, Nov 1971.

52. Thompson, 0. o., Evaluation of Flexible Pavement Behavior with Emphasis on the Behavior of Granular Layers,_ 1969, Ph. D. Disserta­tion, University of Illinois, Urbana, Ill.

53. Morgan, J. R. and Scala, A. J., "Flexible Pavement Behavior and Application of Elastic Theory--A Review," Proceedings, Australian Road Research Board, Vol 4, Part 2, 1968, pp 1201-2143.

54. Barker, W. R., "Nonlinear Finite Element Analysis of Heavily Loaded Airfield Pavement Systems," Proceedings, Symposium on Applications of the Finite Element Method in Geotechnical Engi­neering, Vicksburg, Miss., May 1972.

55. Chou, Y. T., "Evaluation of Nonlinear Resilient Moduli of Unbound Granular Materials from Accelerated Traffic Test Data," FAA-RD-76-65 (TR S-76-12), Aug 1976, U. S. Army Engineer Waterways Experiment Station, CE, Vicksburg, Miss.

56. Turnbull, W. J. and Ahlvin, R. G., "Mathematical Expressions of the CBR (California Bearing Ratio) Relations," Proceedings, Fourth International Conference on Soil Mechanics and Foundation Engineering, 1957.

116

* U.S. GOVEH*ENT PRINTING CX'PICE 1 1977 0.729-321/1379